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A note on the singular value decomposition of idempotent and involutory matrices (2403.05214v1)
Published 8 Mar 2024 in math.NA and cs.NA
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}.
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