MDIV

Purpose:

Solves for a matrix.

Syntax:

MDIV(A, b)

A	-	A non-singular, usually square matrix.
b	-	A matrix

Returns:

A matrix that produces b when multiplied by A.

Example:

W1: {{1, 4, 7},

{2, 5, 8},

{3, 6, 0}}

W2: {1,

W3: W1 *^ W2

{30,

36,

15}

W4: mdiv(W1, W3)

{1,

W5: inv(W1)

{{-1.78, 1.56, -0.11},

{ 0.89, -0.78, 0.22},

{-0.11, 0.22, -0.11}}

W6: W5 *^ W3

{1,

Remarks:

If A, b, and x are matrices, and A *^ x = b, then mdiv(A, b) returns the matrix x.

mdiv(A, b) is equivalent to A \^ b.

MDIV uses LU decomposition to solve for matrix x and is usually more numerically stable than directly calculating the inverse matrix, i.e.

x = inv(A) *^ b

If matrix A is not square, the system is considered a least squares problem and is solved by QR decomposition. The resulting matrix is the best solution in the least squares sense.