Jaromír J. Koliha (2001)
Mathematica Bohemica
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We study block diagonalization of matrices induced by resolutions of the unit matrix into the sum of idempotent matrices. We show that the block diagonal matrices have disjoint spectra if and only if each idempotent matrix in the inducing resolution double commutes with the given matrix. Applications include a new characterization of an eigenprojection and of the Drazin inverse of a given matrix.
Al'pin, Yu.A., Ilyin, S.N. (2005)
Zapiski Nauchnykh Seminarov POMI
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Branislav Martić (1984)
Publications de l'Institut Mathématique
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Mazanik, S.A. (1998)
Memoirs on Differential Equations and Mathematical Physics
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Larsen, Michael (1995)
The Electronic Journal of Combinatorics [electronic only]
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Raphael Loewy (2012)
Open Mathematics
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Let A be an n×n irreducible nonnegative (elementwise) matrix. Borobia and Moro raised the following question: Suppose that every diagonal of A contains a positive entry. Is A similar to a positive matrix? We give an affirmative answer in the case n = 4.
Charles R. Johnson, Robert B. Reams (2016)
Special Matrices
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A copositive matrix A is said to be exceptional if it is not the sum of a positive semidefinite matrix and a nonnegative matrix. We show that with certain assumptions on A−1, especially on the diagonal entries, we can guarantee that a copositive matrix A is exceptional. We also show that the only 5-by-5 exceptional matrix with a hollow nonnegative inverse is the Horn matrix (up to positive diagonal congruence and permutation similarity).
Balaji, R., Bapat, R.B. (2007)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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