# Left Matrix Division

Left Matrix Division (A\B) is defined as solving the equation Ax = B.

Depending on whether A is square, under determined, or over determined, the way to solve
this solution is different. When A is square, `x = inv(A)*b`

. If A is over
determined, the least squares solution is produced. If A is under determined, the least
squares solution with the minimum norm is produced.

\ | Scalar | Row Vector | Column Vector | Matrix |
---|---|---|---|---|

Scalar | Divides the second scalar by the first scalar. | x = A\B solves Ax = B using left matrix division. | x = A\B solves Ax = B using left matrix division. | x = A\B solves Ax = B using left matrix division. |

Row Vector | x = A\B solves Ax = B using left matrix division. | x = A\B solves Ax = B using left matrix division. | ||

Column Vector | x = A\B solves Ax = B using left matrix division. | x = A\B solves Ax = B using left matrix division. | ||

Matrix | x = A\B solves Ax = B using left matrix division. | x = A\B solves Ax = B using left matrix division. |

## Examples

```
4 \ 6
ans = 1.5
[5 4 3] \ [4 6 3]
ans = [0.4 0.6 0.3; 0.32 0.48 0.24; 0.24 0.36 0.18]
[4 2 9; 3 7 4] \ [6; 8]
ans = [Matrix] 3 x 1
0.30303
0.81212
0.35152
```

Invalid examples:

```
[4 2 9; 3 7 4] \ [9 3]
[5 8 3] \ [8; 6; 2]
```

## Comments

Currently, sparse matrices are only supported for an operation on the left-hand side with a full matrix numerator.