Pseudoinverse Calculator

Compute the Moore-Penrose pseudoinverse of a small full-rank matrix (rectangular up to 3x3), used for least-squares solutions when A is not square or not invertible.

Frequently Asked Questions

What is the Moore-Penrose pseudoinverse?

The unique generalization of the matrix inverse that exists for any matrix, square or not. It gives the least-squares solution to Ax = b: x equals A pseudoinverse times b.

When is it equal to the regular inverse?

When A is square and invertible. For a square non-invertible matrix or a rectangular matrix, the pseudoinverse is well-defined but the regular inverse is not.

Why use it in linear regression?

Solving the normal equations beta equals A transpose A inverse times A transpose y is exactly multiplying y by the pseudoinverse of A. It gives the ordinary least squares solution.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.