Moore-Penrose Pseudoinverse

Linear Algebra for Machine Learning · Axiom Academy

The generalized inverse for non-square matrices For non-square matrices (or singular square matrices), we can't compute . The Moore-Penrose pseudoinverse is the generalization: This is the right pseudoinverse for overdetermined systems n)"> Always exists (even if is singular) Breaking down the formula for overdetermined systems: The pseudoinverse connects several key concepts: Least squares solution: minimizes Projection: is the projection matrix onto SVD form: can be computed from singular value decomposition (numerically stable) Underdetermined systems: When , finds the minimum-norm solution

This is the written version of the interactive lesson above. See the full Linear Algebra for Machine Learning course.