A note on the singular value decomposition of idempotent and involutory matrices
Numerical Analysis
2024-03-11 v1 Numerical Analysis
Abstract
It is known that singular values of idempotent matrices are either zero or larger or equal to one \cite{HouC63}. We state exactly how many singular values greater than one, equal to one, and equal to zero there are. Moreover, we derive a singular value decomposition of idempotent matrices which reveals a tight relationship between its left and right singular vectors. The same idea is used to augment a discovery regarding the singular values of involutory matrices as presented in \cite{FasH20}.
Keywords
Cite
@article{arxiv.2403.05214,
title = {A note on the singular value decomposition of idempotent and involutory matrices},
author = {Heike Faßbender and Martin Halwaß},
journal= {arXiv preprint arXiv:2403.05214},
year = {2024}
}