How to find the inverse matrix of a rectangular matrix in Matlab and Octave

To find the inverse matrix of a rectangular matrix on Matlab and Octave use the function pseudo-inverse pinv()

pinv(M)

The parameter M is a rectangular matrix.

The pinv() function calculates the inverse matrix of matrix M.

What is an inverse matrix? A matrix M is invertible and an inverse matrix M^-1 exists if the product M*M^-1 is an identity matrix.

Example

Define a rectangular matrix

>> M=[2 4 1;1 3 2]
M =
2 4 1
1 3 2

Calculate the inverse matrix of M using the function pinv()

>> pinv(M)
ans =
0.315789 -0.289474
0.210526 -0.026316
-0.473684 0.684211

Multiply the matrix M by the result of the pinv (M) function by rounding the product

>> round(M*pinv(M))
ans =
1 0
-0 1

If the result is an identity matrix, the pinv(M) matrix is the inverse matrix M^-1 of the rectangular matrix M.