A note on the singular value decomposition of idempotent and involutory matrices
<|reference_start|>A note on the singular value decomposition of idempotent and involutory matrices: 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}.<|reference_end|>
@article{faßbender2024a,
    title={A note on the singular value decomposition of idempotent and involutory
  matrices},
    author={Heike Fa{ss}bender, Martin Halwa{ss}},
    journal={arXiv preprint arXiv:2403.05214},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.05214},
    primaryClass={math.NA cs.NA}
}