mldivide

Matrix left division `\` of Galois arrays

Syntax

`x = A\B `

Description

`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.

Examples

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.

Limitations

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

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Algorithms

If `A` is an M-by-N tall matrix where M > N, `A \ B` is the same as `(A'*A) \ (A'*B)`.

If `A` is an M-by-N wide matrix where M < N, `A \ B` is the same as `A' * ((A*A') \ B)`. This solution is not unique.

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