Topic: `APLX Help` : `Help on APL language` : `APL Primitives` : `⌹ Matrix divide`
[ Previous | Next | Contents | Index | APL Home ]

`⌹` Matrix divide

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.

Topic: `APLX Help` : `Help on APL language` : `APL Primitives` : `⌹ Matrix divide`
[ Previous | Next | Contents | Index | APL Home ]