Pseudoinverse Calculator

Calculate the Moore-Penrose pseudoinverse of a 2x2 matrix and review the matrix steps beside the result.

Last updated: March 2026 | By ForgeCalc Engineering

Pseudoinverse Solver

Matrix inverse

Matrix A 2x2

Calculation Steps

1.Matrix A = [[1, 2], [3, 4]]

2.Compute A^T A = [[10, 14], [14, 20]]

3.Invert A^T A and multiply by A^T.

4.Result: A+ = (A^T A)^-1 A^T

Pseudoinverse

-2

1.5

-0.5

Moore-Penrose

The Moore-Penrose pseudoinverse generalizes the matrix inverse so you can work with singular or non-square systems in a least-squares sense.

A+ = (A^T A)^-1 A^T

Example: A simple 2x2 matrix produces a 2x2 pseudoinverse.

A+ = (A^T A)^-1 A^T

What happens when the matrix is singular?

This simplified calculator shows an error because a robust SVD-based approach is needed.

Does this accept decimals?

Yes. Any finite real entries are accepted.

Is the pseudoinverse unique?

Yes. The Moore-Penrose pseudoinverse is unique.

Can this solve least-squares problems?

Yes. Pseudoinverses are commonly used for least-squares solutions.

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