2 citations · 2 across the 5 of their papers we have counts for
5 papers
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 to establish a unifying framework for generalized and randomized matrix inverses.…
On the Fundamental Impossibility of Hallucination Control in Large Language Models
Michał P. Karpowicz
Large language models hallucinate. This paper shows when that is unavoidable and what we can do about it. We model inference as an auction of ideas, in which a model's components,…
The Pseudoinverse of is (?)
Michał P. Karpowicz, Gilbert Strang
This paper gives three formulas for the pseudoinverse of a matrix product . The first is sometimes correct, the second is always correct, and the third is almost never corr…
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…
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…