Matrix Divide

is a dyadic function that performs matrix division between two arguments of rank 2 or less. Some dialects automatically apply it to rank-2 subarrays of higher-rank arguments. It shares the glyph Quad Divide  (often called Domino) with the monadic function Matrix Inverse.

Examples
The result of  is equal to , which is analogous to   being equal to. As a consequence,  is true for square matrices.

Applications
From the properties of Moore-Penrose inverse (which Matrix Inverse uses), Matrix Divide can not only be used to solve a system of linear equations, but also to find the linear least squares solution to an overdetermined system.

The following example solves the system of equations $$x + 2y = 5, 2x - y = 8$$. The answer is $$x=4.2, y=0.4$$.

The following example solves the linear least squares over the five points $$(1,5), (2,1), (3,4), (4,2), (5,8)$$. The answer is $$y=1.9 + 0.7x$$.

When used with real vectors as both arguments,  gives the projection of X onto a basis vector Y. The remaining component of X, namely , is orthogonal to Y (  is zero).

Lesson

 * APL Cultivation

Documentation

 * Dyalog
 * APLX
 * NARS2000
 * J Dictionary, NuVoc (as )