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 matrix, in which there are more rows than columns, such that

`A'*A`

is nonsingularA matrix, in which there are more columns than rows, such that

`A*A'`

is nonsingular

Was this topic helpful?