A determinantal inequality for projectors in a unitary space
Abstract: Let be a finite dimensional unitary space and a direct decomposition. Let be the orthogonal projector in with range . If we prove that and if and only if is an orthogonal decomposition.
Let be a normal operator in , of rank . Assume that has rank . If the nonzero eigenvalues of (counting multiplicities) are the same as the nonzero eigenvalues of all together, then for . This generalizes a recent result of L. Brand.
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Keywords: Unitary space, orthogonal decomposition, eigenvalues, eigenvectors, projector, normal operator, hermitian positive definite operator
Article copyright: © Copyright 1971 American Mathematical Society