Diagonalisation of idempotent matrices
نویسندگان
چکیده
منابع مشابه
Block-diagonalisation of Matrices and Operators
In this short note we deal with a constructive scheme to decompose a continuous family of matrices A(ρ) asymptotically as ρ → 0 into blocks corresponding to groups of eigenvalues of the limit matrix A(0). We also discuss the extension of the scheme to matrix families depending upon additional parameters and operators on Hilbert spaces. 1. Matrix theory 1.1. Preliminaries. We first recall some w...
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Let A be a nonnegative idempotent matrix. It is shown that the Schur complement of a submatrix, using the Moore-Penrose inverse, is a nonnegative idempotent matrix if the submatrix has a positive diagonal. Similar results for the Schur complement of any submatrix of A are no longer true in general.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1987
ISSN: 0021-8693
DOI: 10.1016/0021-8693(87)90186-4