This text was written by A. Missoum. The author will appreciate when the readers of this text send him a reasonable donation for his research efforts, to his address: 101 Eddy Street, Hull, Quebec, J8X2W3, Canada. While this text is published on Hans Bodlaender's WWW pages, this does not mean any specific support by Hans Bodlaender for Missoum's proposal of a new notation for chess.
The game of Chess has its origin in the SHATRANJ game . The pieces were named RUKH (ROOK), FARAS (KNIGHT), FIL (BISHOP), FIRZAN (QUEEN), SHEIKH (KING), and BAIDAQ (PAWN). The two games have many similarities, except for the FIL and FIRZAN move, the castling, the Pawn prise en passant, and the optional two squares pawn move at the start of the game, see boards (1), (2). The ancient arab chess players introduced Algebraic, Numerical and Descriptive chess notations in order to record, replay and analyze played games. Some believe that the chess GrandMaster ABU BAKR MUHAMMAD AL SULI (8 th AD) may have invented these notations beside introducing original Openings (TABIATs), Middle (WASAT)), Endgames (MANSUBATS), and many importants chess problems related to mate in TWO, THREE, FOUR, OR FIVE moves. They advised the players to commit these notations to memory. The Arabic letters T, SH, R, M, K, W, Y were associated with the chessboard files a, b, c, d, e, f, g, h, and sometimes F, S, N for a, b, c, d were substituted. The Files were identified algebraically, the rank is named by its file letter and rank number. The descriptive notation (also called english notation) was as follows: KING PAWN (BAIDAQ AL SHEIKH), QUEEN PAWN (BAIDAQ AL FIRZAN), KNIGHT PAWN (BAIDAQ AL FARAS), ROOK PAWN (BAIDAQ AL RUKH), BISHOP PAWN (BAIDAQ AL FIL), KING BISHOP (FIL AL SHEIKH), QUEEN BISHOP (FIL AL FIRZAN), CONNECTED ROOKS (RUKH AL JAMIA), CONNECTED PAWNS (BAIDAQ AL JAMIA), see board (3). While this notation is more precise, it is somehow difficult to read. For this reason the algebraic chess notation was substituted and was internationally adopted and used for chess programming. This method of recording the chess game is also known as the Coordinate or Continental chess notation. Modern chess players adopted two main versions, Full in which both departure and arrival squares are named, and abbreviated, in which the departure square is named only when essential.
BOARD(1) SHATRANJ BOARD(2) CHESS
RU 
FA 
FI 
FZ 
SH 
FI 
FA 
RU 
888888 
R 
N 
B 
Q 
K 
B 
N 
R 
BA 
BA 
BA 
BA 
BA 
BA 
BA 
BA 
888888 
P 
P 
P 
P 
P 
P 
P 
P 
888 

888888 

888 888 

888 

BA 
BA 
BA 
BA 
BA 
BA 
BA 
BA 
888 
P 
P 
P 
P 
P 
P 
P 
P 
RU 
FA 
FI 
FZ 
SH 
FI 
FA 
RU 
888 
R 
N 
B 
Q 
K 
B 
N 
R 
T S B M K W Y N A B C D E F G H
Remark: I will use the letters RU=RUKH (ROOK), FA= FARAS (KNIGHT), FI=FIL (BISHOP), FZ= FIRZAN (QUEEN), SH=SHEIKH (KING), BA=BAIDAQ (PAWN) for the Shatranj game, and R=ROOK, N=KNIGHT, B=BISHOP, Q=QUEEN, K=KING and P=PAWN for the chess game. In the Shatranj, two opponent FIL can never meet each others, and because of the FIRZAN and the FIL moves, the game may take longer than the actual chess. The important pieces in the Shatranj game are the RUKH (ROOK), FIL (BISHOP), FARAS (KNIGHT), while those of the chess are the QUEEN, the ROOK, the, KNIGHT, and the BISHOP. BOARD(3)
1QR 2QR 
1QN 8QN 
1QB 8QB 
1Q 8Q 
1K 8K 
1KB 8KB 
1KN 8KN 
1KR 8KR 
2QR 7QR 
2QN 7QN 
2QB 7QB 
2Q 7Q 
2K 7K 
2KB 7KB 
2KN 7KN 
2KR 7KR 
3QR 6QR 
3QN 6QN 
3QB 6QB 
3Q 6Q 
3K 6K 
3KB 6KB 
3KN 6KN 
3KR 6KR 
4QR 5QR 
4QN 5QN 
4QB 5QB 
4Q 5Q 
4K 5K 
4KB 5KB 
4KN 5KN 
4KR 5KR 
5KR 4QR 
5QN 4QN 
5QB 4QB 
5Q 4Q 
5K 4K 
5KB 4KB 
5KN 4KN 
5KR 4KR 
6QR 3QR 
6QN 3QN 
6QB 3QB 
6Q 3Q 
6K 3K 
6KB 3KB 
6KN 3KN 
6KR 3KR 
7QR 2QR 
7QN 2QN 
7QB 2QB 
7Q 2Q 
7K 2K 
7KB 2KB 
7KN 2KN 
7KR 2KR 
8QR 1QR 
8QN 1QN 
8QB 1QB 
8Q 1Q 
8K 1K 
8KB 1KB 
8KN 1KN 
8KR 1KR 
BOARD(4) NUMERICAL NOTATION
57 
58 
59 
60 
61 
62 
63 
64 
49 
50 
51 
52 
53 
54 
55 
56 
41 
42 
43 
44 
45 
46 
47 
48 
33 
34 
35 
36 
37 
38 
39 
40 
25 
26 
27 
28 
29 
30 
31 
32 
17 
18 
19 
20 
21 
22 
23 
24 
9 
10 
11 
12 
13 
14 
15 
16 
1 
2 
3 
4 
5 
6 
7 
8 
.This notation was used by the arabs to describe the FIL, FARAS, RUKH and FIRZAN tours
The Arabs also devised the following notation related to tactic and
strategy position see Board(5).
1:0 
0:2 
1:1 
0:1 
1:0 
0:2 
1:1 
0:1 
1:1 
1:0 
0:1 
2:0 
1:1 
1:0 
1:1 
2:0 
1:1 
0:1 
1:0 
0:2 
1:1 
0:1 
1:0 
0:2 
0:1 
2:0 
1:1 
1:0 
0:1 
2:0 
1:1 
1:0 
1:0 
0:2 
1:1 
0:1 
1:0 
0:2 
1:1 
0:1 
1:1 
1:0 
0:1 
2:0 
1:1 
1:0 
0:1 
2:0 
1:1 
0:1 
1:0 
0:2 
1:1 
0:1 
1:0 
0:2 
0:1 
2:0 
1:1 
1:0 
0:1 
2:0 
1:1 
1:0 
For example, the squares 2:0 in d7 indicates that white could attack twice this square, while the squares 0:1 in c3 mean that black could attack this square once. This notation can be viewedas the pieces view of the board (that is the pieces are watching the square of the board in order to occupy them) and or the board view of the pieces (that is the squares of the chessboard are watching the pieces coming to attack, or occupy them.).
Lets mention that in an ancient arab manuscript, the invention of the Shatranj (Chess) is described as follows:
# The inventor of chess made the board to represent a field of battle upon which two armies are drawn up for contest, and the six figures, Sheikh, Firzan, Fil, Faras, Rukh and Baidaq represent the six classes upon which war was turns and which are essential to it. Of these the first is the King who rules, the second the vizier who advise, the third the commander of the army who arranges, the fourth the cavalry, the fifth the fortress (Husun) and the sixth is the infantry. He represented the King by the Sheikh, the Vizier by the firzan, the commander of the army by the Rukh, the cavalry by the Faras, the fortress by the Fil, and the infantry by the Baidaqs. This is the classification of the chessmen (ALAT AL SHATRANJ. The following was his intention in the arrangement . He puts the Sheikh in the centre because the King ought to be in the heart of the army. He put the Firzan next to him because the strongest places in the battle array ought to be where King and Vizier are. He put the Faras between Fil and Rukh because cavalry ought to be at the defense of the fortresses. He put the rukh next to the Faras because the commander ought to be in command of the right and the left wings. He puts the Baidaq in a line front of these because the infantry is placed in the van of the battle. This was his intention in the arrangement of the chessmen. His intention in the arrangement of the pieces in the game was to be to a struggle and attack. He gave the Baidaq a move of one square in a straight line. Because it is not right for the footsoldier to quit his position in battle, nor to advance except step by step. He made it take obliquely because the injury he inflicts on his enemy in the battle happens unexpectedly. He appointed that he should become a Firzan when he reached the end of the board, because a man who advances and penetrates to the enemys camp, and preserves himself from capture or overthrow, deserves the viziership in war. He gave the Faras a far reaching move, because the horsemen, being mounted, can transport himself to a distance, and can fall back to his camp when he is threatened. He made his moveas oblique one in moving forwards and backwards and in capturing, because the horsemen of necessity attacks his enemy, lance in hand, and takes him by swift and sudden movements. He gave the rukh the move in the four cardinal directions as far as the end of the lines confronting him, which is the most extended move of the pieces, because in war it is the commander of the right and the left wings who haras and burden to their utmost the enemy weaks points which are opposite to them. He made the Sheikhs move a single square in every direction, because the King is not one who should move swiftly. He is free to move at choice either forwards or backwards. The rule for the Firzan is the same, except that his liberty of move is less than the Sheikh s. When he takes, he takes according to his ward...#
(see A.J.R. MURRAY, History Of Chess )
This text gives a precise parallelism between Shatranj (Chess) and the war where cavalry, elephants, commanders, Fortresses, King and Infantry were involved.
Now after this breve historical introduction, I will introduce my Matrix Chess Notation and show its advantages over the classical algebraic chess notation
MATRIX CHESS NOTATION
Lets recall that a n x k matrix is simply a rectangular board of n columns
and k rows written:
C11 C12 C13 ... C1n
C21 C22 C23 ... C2n
(C)= (Cij)_{ 1 I N}
_{1 J K} C31 C32 C33 ... C3n
.......................................
.......................................
Ck1 Ck2 Ck3 ... Ckn
The Cij are called the components of the matrix, and they can be numbers,
functions, matrices, block of matrices or else.
Example 2 5 6 7
3 4 9 1
6 2 8 4
is a 4x3 rectangular matrix and its components are numbers.
In our case, we will consider the following rectangular (or square) matrix types:
1 2 3 ... ... n2 n1 n
WB11 
WB12 
WB13 
...... 
..... 
WB1n2 
WB1n1 
WBn 
WB21 
WB22 
WB23 
.... 
.... 
WB2n2 
WB2n1 
WB2n 
WBij 

WBk11 
WBk12 
WBk13 
WBk1n2 
WB k1n1 
WBk1n 

WB k 1 
WB k 2 
WB k 3 
WB k n2 
Wb k n1 
Wbk n 
where WBij is the ij th move of white, resp black, and W, B stand for white, resp black pieces of the chess. Now, for purely practical reasons, we will write the components WBij, 1 i n, 1 j k of the chess matrix as follows:
M S
WBij
G U
which means that at the ij th move, white moves from the squares G to M, resp black moves from the squares U to G, where G, M, U, S can be any of the chess board squares
ai, bi, ci, di, ei, fi, gi, hi, i=1,2,3,4,5,6,7,8, and W, B are anyone of the pieces K=King, Q=Queen, R=Rook, N=Knight, B=Bishop, P=Pawn
Example: f3 f8 signifies that white Knight moves from the squares g1 to f3
NB resp Black Bishop moves from squares c8 to f8
g1 c8
We will adopt the following rules:
RULE1 If at a ij th move, white, resp black have the same denomination, we will simply consider the symbol of one of the two pieces
Example: a7 d3 Means that white Rook moves from squares a1 to a7
R resp black Rook moves from sqaures d7 to d3
a1 d7
RULE2 The pawn move is simply represented by the column letter he occupies
Example: 4 5 Means that white pawn moves from squares c2 to c4
cd and black pawn moves from squares d7 to d5
2 7
5 6 Means that white pawn moves from e4 to e4, and
e Black pawn moves from e5 to e6
4 5
RULE3 If at the ij th move, White, or black, or both make a piece (pawn) capture, it will be put at the upper corner of the matrix component
Example: Pa6 Bf3 means that White Rook captures a black pawn at a6, resp
RN Black Knight captures a white Bishop at f3
d1 g1
If both side capture a pawn or a piece we will write that piece (pawn) in between the arrival squares of white and blackof the corresponding matrix component.
Example: a6 P f3 Means that white rook captures a black Pawn at a6
RN resp., black Knight captures a white Pawn at f3
d1 g1
RULE 4 We will use the following chess symbolism
! Good move, !! Excellent move, Bad move, ?? Blunder
o Kings side castling, O Queens side castling, # mate, + Check, ++ double check, 1/0 White win, 0/1 black win, 1/2 1/2 draw. !? Move of doubtful value, Ad Ad libidum, Ep en passant
Remark : in the matrix chess notation we dont use the signs x for capture, and OO for small castling, OOO for the great castling.
RULE 5 We will use the following abbreviations (optional) for the well known chess openings on top of the four or five components of the matrix chess notation.
AL = ALEKHINE, BE = BENONI, BI = BIDONI, EN = ENGLISH, GN = GRUNFELD, EI = EAST INDIAN, WI = WEST INDIAN, KG = KING GAMBIT, QG= QUEEN GAMBIT, EV = EVANS GAMBIT, SG = SCOTISH GAMBIT, IT = ITALIAN, 2N = TWO KNIGHTS, 3N = THREE KNIGHTS, 4N = FOUR KNIGHTS, NE = NETHERLAND, SL = SLAVIC, RU = RUSSIAN, PE =PETROFF, NI = NIMZOVITCH, MO= MORRA GAMBIT , PI = PIRC, PH = PHILIDOR, BG = BOUGOLIAGOV, TC = TCHIGORINE, CK = CARO KAHN, VI= VIENNESE, BR = BERLIN, OR=ORTHODOX, SK = SCANDINAVIAN, RU = RUIZ LOPEZ, PA=PAULSEN, CH= SCHEVENINGE, SI= SICILIAN, DR= DRAGON, SA= SEAMISCH, LE= LETTON, FR= FRENCH, MG=MARSHALL GAMBIT, BR= BAIRD, RA= RAUSER, FA= FALKBEER, PO= PONZIANI, etc...
Now, lets consider an arbitrary chess game and apply it the algebraic and matrix chess notations. I have chosen the following short and concise chess game commented by the French chess GrandMaster and world champion ANDRE FRANCOIS PHILIDOR (1847). The algebraic notation of this game is the following
1 e4 e5 2. Bc4 c6 3. D4 e x d4 4. Qxd4 d6 5.f4 Be6 6.Bd3 d5
7. e5 c5 8. Qf2 Nc6 9. c3 g6 10 h3 h5 11 g3 Nh6 12. Nf3 Be7
13. a4 Nf5 14.Kf1 h4 15. G4 Ng3+ 16 Kg2 Nxb1 17.Kxh1 Qd7
18. Qg1 a5 19. Be3 b6 20. Na3 000 21 Ba6+ Kc7 22 Nc2 Ra8
23 Bf5 Qd8 24 b4 Qf8 25 bxc5 cxc5 26 Nd2 c4 27 Nf3 f6
28 Bb6+ Kb7 29 Bxc6 Kxc6 30 Ncd4+ Kd7 31 f5 Bg8 32 e6+ Ke8
33 Nb5 Bd6 34 Qd4 Black Resign
Philidor commented this game as follows: 3.d4 you must push this pawn twice to prevent the opponent from advancing his pawns to the center. And play d7d5, thus attacking your bishop and gaining adavantage. If he plays d7d5 this will totally change the game.
5...Be6 he plays this bishop to advance his queens pawn and leave space for his king bishop and may capture it. 8.... Nc6 If instead of developing this piece, he will continue to adavance his pawns, he will lose the game. In this situation, you have four pawns against his three pawns on the kings side, and three pawns against his four pawns on the queen side. The player who first will separate the pawns oh his oppoent where they are in majority will win the game.
11. g3 this move is essential because by playing h4, black will cut the communication between your pawns on the king side.
Remark : Usually, the comments follows the moves. But I preferes to write them at the bottom of the algebraic chess notation.
Now, Philidor chess game can be written in Matrix Chess Notation as follows:
PH 
1 2 3 4 5 6 7
4 5 e 2 7 
c4 6 Bc f1 7 
4 Pd4 de 2 5 
* 6 Qd d1 7 
4 e6 fB 2 c8 
d3 5 Bd c4 6 
5 5 ec 4 6 
Board of pieces position 
f2 c6 QN d4 b8 
3 6 cg 2 7 
3 5 h 2 7 
3 h6 gN 2 g8 
f3 e7 NB g1 f8 
4 f5 aN 2 h6 
f1 4 Kh e1 5 
Board of pieces position 
4 g3 gN+ 3 f5 
g2 Rh1 KN f1 g3 
Nh1 d7 KQ g2 d8 
g1 5 Qa f8 7 
e3 6 Bb c1 7 
a3 NO b1 
a6 c7 +BK d3 c8 
Board of pieces position 
c2 a8 NR a3 d8 
b5 d8 BQ a6 d7 
4 f8 bQ 2 d8 
Pc5 b 4 5 
d2 4 Nc f3 5 
f3 6 Nf d2 7 
b6 b7 +BK e3 C7 
Board of pieces position 
N c6 B +BK b5 b7 
d4 d7 +NK c2 c6 
5 g8 fB 4 e6 
6 e8 +eK 5 d7 
b5 d6 NB d4 e7 
d4 Q. f1 1/0 
Board of pieces position 
COMMENTS: 3d4 This prevent your opponent from posting
the pawn at the center and with d5 he will attack your bishop. 5...Bc6
will oppose your King bishop and later captures it or he will push his
King pawn and leaves space for his King bishop. 8... Nc6 If he continues
to push forwards his pawns, he4 will lose the game. 10... h5 He pushes
this pawn in order to prevent yours from advancing, etc...
Now what are the advantages of this matrix Chess notation over the classical
algebraic chess notation. There are many.
1) The matrix chess notation is more visual than the algebraic chess notation. It is simply written as a board which directly shows the respective pieces moves of white and black.
The pieces (pawns) capture is directly seen at the upper corner of each matrix component. Hence one can have a quick idea about the material balance between white and black. For example, at the end of the first row of the matrix chess notation of Philidor game, we see that both white and black captured one pawn. So, after seven moves, there is a material balance between white and black
2) At the end of each row of the matrix is set a chess board with piece positions of white and black.(see the above matrix chess notation). This gives a direct view of the positional fighting aspect between white and black, without the need of puting the pieces on the chessboard. One can therefore analyze the played chess game from the pieces position at the end of each row (or group of seven moves ) of the matrix chess notation. Also, at any ij th move of white, resp black the player can exactly figure out the piece position of his pieces and tghose of his opponent on the chessboard. For example, at the 11 th move, it suffices to consider the board of pieces position at the end of the first row and add it the 8th, 9th, 10th and 11 th move of white resp black.
3) At the top of the left of the first row of the matrix are put the chess opening and defense types So, the player have a first idea about the opening and defense types used by white and black.
4) The reader can point any one of the matrix chess component and exactly knows the ij th move of white and black. For eample, the intersection of the fourth column and the third row of the matrix chess is the 14 + 4 = 18 th move of white, resp black.
5) The chess comments are put at the bottom of the matrix, and this will clearly distinguish between the moves and the comments. On the other hands, In the algebraic chess notation, the mixing of the moves and the comments create some confusion for the ordinary chess player.
6) Reading the algebraic chess notation is like reading a page of a roman or a book. The player has to go through all the line step by step in order to understand the game. Sometimes someone has to go more times over a same line to follow the game. This constitutes a handicap for the ordinary chess player.
7) The matrix chess notation gives a direct view of the frequency of the pieces and pawns move
Thus we directly see from the matrix chess notation, that in Philidor chess game, white used 13 times the pawn, 7 times the Bishops, 7 times the Knights, 3 times the Queen and 3 times the King, while Black used 14 times the Pawn, 4 times the Bishops, 5 times the Knights, 1 time the Rook, 2 times the Queen and 5 times the King. So, the chess battle between white and black was mainly a pawn battle as pointed by Philidor The Pawns are the soul of the game. .. Nevertheless, it must be understood that Philidor meant that the chess plan must be built for the sole promotions of the pawns, and not that the pawns are better than the pieces.
8) From the matrix chess notation, we can directly extract the matrices
of pieces, or the squares used by white, resp black. This will give a more
understanding of the game. Thus in Philidor game, the matrices of pieces
and squares used of white are:
Pe4 Bc4 Pd4 Qd4 Pf4 Bd3 Pe5
Qf2 Pc3 Ph3 Pg3 Nf3 Pa4 Kf1
Pg4 Kg2 Kh1 Qg1 Be3 Na3 Ba6 MATRIX of pieces used
Nc2 Bf5 Pb4 Pc5 Nd2 Nf3 Bb6
Bc6 Nd4 Pf5 Pe6 Nb5 Qd4
This matrix gives an idea of the pieces view of the board ( ie the pieces watching to occopy the squares of the chess board)
e4 c4 d4 d4 f4 d3 e5
f2 c3 h3 g3 f3 a4 f1 Matrix of the square
g4 g2 h1 g1 e3 a3 a6 Used
c2 f5 b4 c5 d2 f3 b6
c6 d4 f5 e6 b5 d4 .
This matrix gives the board view of the pieces by white (i.e. the squares of the board are watching the pieces coming to occupy them, or attacking them). So, from the matrix of the pieces used, we see that white started by ocuppying e4, then opened a line for the queen by c4, then move to d4 to control the center, then start a right flank move, etc. So, a precise analysis of the game could be focused on the matrix of pieces move and the matrix of the squares used by white and black.
9) Another flexibility of the matrix chess notation is that the chess
game can be seen as a game of vectors move (group of moves) instead of
single moves as for the algebraic chess notation.Thus Philidor chess game
can be viewed as a game of seven successive vectors moves (rows move) of
white, resp black So, one can analyze Philidor game in terms of group of
moves . This will add more extension of the tactic, strategy, pieces position,
and the plan of the game.Thus, Philidor chess game can be seen as a game
of five successive vector moves instead of 34 successive single moves:
The vectors move of white can be designated by the vectors
V1 = (Pe4 Bc4 Pd4 Qd4 Pf4 Bd3 Pe5 )
V2 = (Qf2 Pc3 Ph3 Pg3 Nf3 Pa4 Kf1 )
V3 = (Pg4 Kg2 Kh1 Qg1 Be3 Na3 Ba6 )
V4 = ( Nc2 Bf5 Pb4 Pc5 Nd2 Nf3 Bb6 )
V5 = ( Bc6 Nd4 Pf5 Pe6 Nb5 Qd4 )
10) We can also partition the matrix chess notation into a matrix of matrices, or a matrix of vectors. For example, Philidor chess game cab be viewed as a matrix of four matrices of moves:
or else
A B
4 5 e 2 7 
c4 6 Bc f1 7 
4 Pd4 de 2 5 
* 6 Qd d1 7 
4 e6 fB 2 c8 
d3 5 Bd c4 6 
5 5 ec 4 6 

f2 c6 QN d4 b8 
3 6 cg M! 2 7 
3 5 h 2 7 
3 h6 gN 2 g8 
f3 e7 NB M2 g1 f8 
4 f5 aN 2 h6 
f1 4 Kh e1 5 

4 g3 gN+ 3 f5 
g2 Rh1 KN f1 g3 
Nh1 d7 KQ g2 d8 
g1 5 Qa f8 7 
e3 6 Bb c1 7 
a3 NO b1 
a6 c7 +BK d3 c8 

c2 a8 NR a3 d8 
b5 d8 BQ N3 a6 d7 
4 f8 bQ 2 d8 
Pc5 b 4 5 
d2 4 Nc M4 f3 5 
f3 6 Nf d2 7 
b6 b7 +BK e3 C7 

N c6 B +BK b5 b7 
d4 d7 +NK c2 c6 
5 g8 fB 4 e6 
6 e8 +eK 5 d7 
b5 d6 NB d4 e7 
d4 Q. f1 1/0 
C D
11) Because of the geometric properties (reflection, translations, rotations) of matrices, one can also apply them to the matrix chess notation .Thus one can apply reflections of the matrix about its diagonals, or me dian lines and read the matrix chess notation differently Thus, a reflection of the matrix chess notation about its line diagonal AD gives the new matrix notation:
d4 Q f1 1/0 
b5 d6 NB d4 e7 
6 e8 +eK 5 d7 
5 g8 fB 4 e6 
d4 d7 +NK c2 c6 
N c6 B +BK b5 b7 

b6 b7 +BK e3 C7 
f3 6 Nf d2 7 
d2 4 Nc f3 5 
Pc4 Pc5 b 4 5 
4 f8 bQ 2 d8 
b5 d8 BQ a6 d7 
c2 a8 NR a3 d8 

a6 c7 BK d3 c8 
a3 NO b1 
e3 6 Bb c1 7 
g1 5 Qa f8 7 
Nh1 d7 KQ g2 D8 
g2 Rh1 KN f1 g3 
4 g3 QN 3 f5 

f1 4 Kh e1 5 
4 f8 aN 2 h6 
f3 e7 NB g1 f8 
3 h6 gN 2 g8 
3 5 h 2 7 
3 6 Og 2 7 
f2 c6 QN d4 b8 

5 5 ec 4 6 
d3 5 Bd c4 6 
4 e6 fB 2 c8 
Pd4 6 Qd d1 7 
4 Pd4 de 2 5 
c4 6 Bc f1 7 
4 5 e 2 7 
This is simply the backward play of Philidor chess game. Reading backward the chess game gives more understanding of the game .
12) From the matrix chess notation one can read the chess game row by row, column by column, from bottom to top, or top to bottom, left to right or right to left.
13) Since each component of the matrix chess notation is simply the addition of a ij th move of white and black to the previous i1, j1 th moves, then the matrix chess notation can be viewed as a matrix of positions for white, resp black
P11 P12 P13 P14 ... P1 n2 P1 n1 P1n
P21 P22 P23 P24 ... P2 n2 P2 n1 P2n
P31 P32 P33 P34 ... P3 n2 P2 n1 P3n
................................................................................
................................................................................
Pk1 Pk2 Pk3 Pk4 Pk n2 Pk n1 Pkn
Where each Pij 1 i n, 1 j k Is the ij th position of white respectively black pieces. One can therefore write computer programs which when one clicks on a ij th component of the matrix chess notation, this will automatically gives the associated ij th pieces position of white, resp black . Thus Philidor chess game can be seen as the matrix of positions:
P12 P12 P13 P14 P15
P21 P22 P23 P24 P25
P31 P32 P33 P34 P35
P41 P42 P43 P44 P45
P51 P52 P53 P54 P55
So, one can switch on and off from chess matrix components to pieces position on the chessboard and vice versa. We can write computer programs to switch from the matrix of pieces moves to the matrix of squares used by white and black. Also, Now, each board position Pij of the matrix of positions can be seen as a vector V= (CP, IP, SP, DP, GB, BB, GN, BN, SK, UK, CS, UC, OL, OD, SP, TE, DV, CR, PN, QC, etc...) where CP =Connected pawns, IP= Isolated pawns, DP = Doubled pawns, GB = Good bishop BB= Bad bishop, GN= Good Knight, BN = Bad Knight, SK= King secure, UK= King unsecure CS= Castling, UC= Uncastling, OL= Open line, OD=Open diagonal, SP=Space of manoeuvring UP= Not manoeuvring space, TE= Tempo, DV= Piece development, CR = Connected rooks, Posting Knight, Queen centralization, etc then the matrix of pieces position on the chessboard can be converted into a matrix of matrix blocks where each position Pij is itself a matrix block. This will add more understanding and interpretation of the played chess game.
Lets mention that modern approach on tactic and strategy ( STEINIZ ) consider:
Motivated attack based on a number of favorable characteristics which they justify it.
More freedom of manoeuvring, Center occupation or control, vulnerable position of the opponent King, Weak points (squares, lines and diagonals), Better pawn structures, majority of pawns on wing sides, good bishops and Knights, Bad bishop and Knights, Connected Rooks, Centralization, posting pawns, matrial adavantage, overprotection, blocus, prophylaxis,..
Principle of accumulation, an attack is motivated only and only if the position is superior to the opponent, and when it become imparative to convert the plus values into effect. If both sides have balanced positions, wait and multiply the plus values to provocate the balance rupture into an advantage.
The reader could practice applying the matrix chess notation to this following game
1 e4 c6 2 d4 d5 3 exd5 c x d5 4 Bd3 Nc6 5 c3 Nf6 6 Bf4 Bg4 7 f3 Bh5
8 Ne2 e6
9 Nd2 Bd6 10 Bg3 Qc7 11 Nb3 Bg6 12 Rc1 Bxd3 13 Qxd3 00 14 Bxd6 Q x
d6
15 00 Rfe8 16 Ng3 g6 17 Rce1 Rac8 18 Re2 Nb8 19 a4 Nfd7 20 a5 Qa6
21 Qxa6 bxa6 22 Ra1 Rc7 23 Nc1 Rec8 24 Nd3 Rb7 25 Ra3 Nc6 26 Nf1 Rb5
27 b4 Nd8 28 Ne3 Rbb8 29 Kf2 Nb7 30 Nc5 Ndxc5 31 bxc5 Nd8 32 f4 Nc6
33 Ng4 Rb1
34 Ne5 Nxe5 35 f x e5 Kf8 36 Ke3 Rcb8 37 Rf2 Ke7+ 38 Rc2 Kd7 39 Raa2 Ra8
40 Kd3 Rd1+ 41 Rd2 Rc1 42 Rac2 Rcb1 43 Rf2 Ke7 44 c6 Rb8 45 c4 Rb3 +
46 Rc3 d x c4 47 Kxc4 Rb4 48 Kd3 Re8 49 Ke3 Rb5 50 Ra2 Rf8 51 g4 Kd8
52 c7+ Kc8 53 Rf2 Rxa5 54 Rc6 Ra3+ 55 Ke4 Kd7 56 Rxf7+ Kxc6 57 Rxf8
Kxc7
58 Rf7+ Kd8 59 Rxh7 g7 60 Rg7 Ra2 61 Rxg5 Rxh2 62 Rg8+ Kc7 63 Rg6 a
64 Rxc6 Kb7 65 Rf6 Rg2 66 e6 Rxg4+ 67 Ka5 Kc7 68 Rf7+ Kd8 69 Rxa7 Rh4 70
Kc5 Black resign
SULTAN KHAN (19051966). He was born in the PUNJAB (India) and he learned chess at the age of nine. In 1929 we won the all championship of India. Then in London he won the British championship. Then he started to defeat many leading Chess GrandMasters. He came second after Tartakover and third after Capablanca in the Hasting tournament (1931). Later he left Europe to India where he remained for the rest of his life. Capablanca called Sultan Khan a genius. Here follows a chess game between Sultan Khan and Flohr (CaroKahn defence).
Now we can rewrite this game in matrix chess notation as follows:
14) Another advantage of the matrix chess notation is that we can also apply it to the chess descriptive notation as follows: Consider the following CapablancaFine chess game: written in descriptive chess notation
1PQ4 NKB3 2 PQB4 PK3 3NQB3 PQ4 4.BN5 QNQ2 5.PK3 BK2 6.NB3 PB4 7.PxQP BpxP 8.QxP PxP 9BN5 OO 10.KBxN BxB 11.BxN BxB 12QxQP QB1 13.NQ4 RQ1 14.OO BB3 15.QQB5 BK1 16.Qx Q QrxQ 17.KRQ1 PKN3 18.N/4K2 KB1 19.RxR RxR 20RQ1 RxR ch 21 NxR KK2 22 N/1B3 BN2 23 NQ4 KQ3 24 KB1 KB4 25N/4K2 KB5 26 KK1 KQ6 27 KQ1 BxN1! 28 NxB BB3 29 NK2 BR sch! 30 PN3 BB3 31 PKR4 PB3 32 NB4ch KB6 33 KB1 PKN4! 34 PxP PxP 35 NK6 BxP 36 NxP PKR4! 37 KQ1 PR5 38 KK2 PR6 39 PB3 PR7 40 NK4ch PR7 41 NB2 PR8/q 42 NxQ KB6 44 PK4 KQ5 45 PR3 PR4 46 PR4 PN3 47 KN3 KK8 48 PK5 BxP black resigns
This game can be written in matrix chess notation as follows:
1 2 3 4 5 6 7 8
Q4 B3 PN 
B4 K3 P 
B3 Q4 NP Q 
N5 Q2 BQ Q 
K3 K2 PB 
B3 B4 NP 
P (PB) Q P 
P (QP) 
N5 Bo 
N B (B) 
N B (B) 
P B1 x Q Q 
Q4 Q1 NR 
B3 oB 
B5 K1 QB Q 
Q (Q) R 
Q1 N3 RP K K 
K B1 NK 4 
R (R) 
Q1 R Rx 
R K2 xNK 
B3 N2 NB 
Q4 Q3 NK 
B1 B4 K 
K2 B5 NK 4 
K1 Q6 K 
Q1 N KBx 
B B3 xNB 
K2 R5 NB+ 
N3 B3 PB 
R4 B3 P K 
B4 B6 + NK 
B1 N4 KP! K 
P (P) 
K6 P Nbx 
P R4 xNP! K 
Q1 R5 KP 
K2 R6 KP 
B3 R7 P 
K4 N5 +NP 
B2 Q NP R8 
Q N (NB) 
B2 B6 K 
K4 Q5 PK 
R3 R4 P 
R4 N3 P 
N3 K8 K 
K5 P PBx 
In conclusion : The matrix chess notation possesses many advantages
over the classical algebraic chess notation.