Matrix left division \ of Galois arrays
x = A\B
x = A\B divides the Galois array A into B to produce a particular solution of the linear equation A*x = B. In the special case when A is a nonsingular square matrix, x is the unique solution, inv(A)*B, to the equation.
The code below shows that A \ eye(size(A)) is the inverse of the nonsingular square matrix A.
m = 4; A = gf([8 1 6; 3 5 7; 4 9 2],m); Id = gf(eye(size(A)),m); X = A \ Id; ck1 = isequal(X*A, Id) ck2 = isequal(A*X, Id)
The output is below.
ck1 = 1 ck2 = 1
Other examples are in Solving Linear Equations.
The matrix A must be one of these types:
A nonsingular square matrix
A tall matrix such that A'*A is nonsingular
A wide matrix such that A*A' is nonsingular