Michał P. Karpowicz

activity

20212026

most citedOn the Fundamental Impossibility of Hallucination Control in Large Language Models

2 citations · 2 across the 5 of their papers we have counts for

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4 papers · 1 filter

math.NA2026

Generalized Inverses of Matrix Products: From Fundamental Subspaces to Randomized Decompositions

Michał P. Karpowicz, Gilbert Strang

We investigate the Moore-Penrose pseudoinverse and generalized inverse of a matrix product $A = C R$ to establish a unifying framework for generalized and randomized matrix inverses.…

math.NA2023

The Pseudoinverse of $A = C R$ is $A^{+} = R^{+} C^{+}$ (?)

Michał P. Karpowicz, Gilbert Strang

This paper gives three formulas for the pseudoinverse of a matrix product $A = C R$ . The first is sometimes correct, the second is always correct, and the third is almost never corr…

math.NA2023

The secret life of matrix factorizations: how matrix decompositions reveal and keep secrets of linear equations and what we can do about it

Michał P. Karpowicz

This paper explores the relationship between matrix factorizations and linear matrix equations. It shows that every matrix factorization defines two hidden projectors, one for the…

math.NA2021

A theory of meta-factorization

Michał P. Karpowicz

Meta-factorization asks how different factors and transforms describe the same matrix and how a factor can be replaced while preserving that matrix. Projector and reconstruction eq…

Generalized Inverses of Matrix Products: From Fundamental Subspaces to Randomized Decompositions

The Pseudoinverse of A=CR is A+=R+C+ (?)

The secret life of matrix factorizations: how matrix decompositions reveal and keep secrets of linear equations and what we can do about it

A theory of meta-factorization

The Pseudoinverse of $A = C R$ is $A^{+} = R^{+} C^{+}$ (?)