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.

Table 1.
\	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.