A note on the singular value decomposition of idempotent and involutory matrices
Abstract
It is known that singular values of idempotent matrices are either zero or larger or equal to one 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 FasH20.
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