Are there any applications of matrices, or linear algebra to chess? If so, are there good books on it? Chess has never had any appeal to me, but recently my brother bought a chess set, and I realized that the board can be represented as an 8x8 matrix, and each type of of piece as a number from 0 to 6, the 6 pieces, and the empty square. So I've been looking for some info on the internet, but I haven't found too much. Do you know if anybody has made some research on this, or published books, or articles. Matrices have applications on stochastic processes, optimization, best-decision taking, so wouldn't it be possible to create models for best moves according to a situation, and such?
What do you think? 
 A: Taking a bit of a stab in the dark...  It seems to me unlikely that matrices could be used in the way you describe for chess.  The basic operations on matrices are addition, multiplication by numbers and multiplication of matrices.  Just to take addition, it would mean something like this: if one position has a king on a1 and another has a queen on a1 then "adding" them gives a position with a bishop on a1 (for example).  This doesn't really seem to make any kind of sense in terms of actually playing chess.
On the other hand, linear algebra has huge applications (as you have mentioned) and I wouldn't be surprised if matrices are used in chess programming.  But not, I think, in the way you have described.
A: Linear algebra has been applied to chess endgames in the following paper: http://library.msri.org/books/Book29/files/stiller.pdf. 
-Roger Bilisoly
A: The main problem with trying to represent a chess game as a series of matrices (each representing a state of the board between consecutive moves) is that while it is fairly trivial to represent the board as such, it is not conducive to generating such a board through matrix multiplication.
I just spent a few hours over the past couple of days trying to do this and eventually found this on Google after I realised it can't work.
The main problem is that Matrix multiplication to go from one matrix to another relies on computing the inverse of the initial matrix so that it is 'cancelled out' before moving to the next matrix.
Unfortunately, you can't compute the inverse of a matrix that has identical rows (meaning it has a zero determinant).
Whether you organise a chess board vertically or horizontally, either the middle ranks begin identical (all empty) or the outer files appear identical (Rook,pawn,empty,empty,empty,empty,-pawn,-Rook / Bishop, pawn, empty,empty,empty,empty,-pawn,-Bishop).
You could do the stepping between states by matrix addition, but it's less appealing computationally.
