⌹ 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 ⌹ Y
       1          2
       2          4
       6          4

This last operation is the same as

             ( ⌹ 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 ⌹ 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.