## Ž Matrix divide

Two-argument form See also one-argument form Matrix inversion

The right and left-hand arguments are conformable simple numeric matrices (arrays of rank 2). Vectors are treated as one column matrices and scalars are treated as matrices of shape 1 1. The result is a matrix which, if matrix- multiplied by the right-hand argument, would yield the left-hand argument.

                 X
           1  2
           3  6
           9 10
                 Y
           1 0 0
           1 1 0
           1 1 1
                 X Ž Y
           1          2
           2          4
           6          4

This last operation is the same as

                 ( Ž Y ) +.× X

which is another way of defining the operation.

An important use for matrix divide is to give the least squares solution to the set of simultaneous linear equations:

                 B = A +.× X             for a matrix A and vector B, or columns of
                                          matrix B

The solution is:

                 B Ž A

If the matrix division does not have a solution, DOMAIN ERROR will be reported. Note that matrix division is subject to accuracy limitations imposed by the representation of floating-point numbers and the algorithm used to calculate the result.

Topic: APLX Help : Help on APL language : APL Primitives : Ž Matrix divide

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