# Reverse Cholesky factorization and tensor products of nest algebras

## TL;DR

This paper establishes a new factorization result for certain positive semidefinite matrices over natural numbers and extends known results on tensor products of nest algebras, using reproducing kernel Hilbert space theory.

## Contribution

It introduces a novel factorization theorem for matrices with specific sparsity patterns and generalizes existing results on tensor products of nest algebras.

## Key findings

- Positive semidefinite matrices can be factored as upper times lower triangular matrices.
- Extended factorization results to tensor products of nest algebras.
- Used reproducing kernel Hilbert space theory in proofs.

## Abstract

We prove that every positive semidefinite matrix over the natural numbers that is eventually 0 in each row and column can be factored as the product of an upper triangular matrix times a lower triangular matrix. We also extend some known results about factorization with respect to tensor products of nest algebras. Our proofs use the theory of reproducing kernel Hilbert spaces.