2011•Moscow University Computational Mathematics and CyberneticsRequires access

On almost normal matrices

Х. Д. Икрамов

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Abstract

An almost normal matrix is defined as an n by n matrix having n − 1 mutually orthogonal eigenvectors. The properties of these matrices are shown to be intermediate between the properties of conventional normal matrices and those of general matrices. In particular, the Schur form of an almost normal matrix can in a certain sense be considered canonical.

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What this paper is about

An almost normal matrix is defined as an n by n matrix having n − 1 mutually orthogonal eigenvectors. The properties of these matrices are shown to be intermediate between the properties of conventional normal matrices and those of general matrices. In particular, the Schur form of an almost normal matrix can in a certain sense be considered canonical.

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Available abstract

An almost normal matrix is defined as an n by n matrix having n − 1 mutually orthogonal eigenvectors. The properties of these matrices are shown to be intermediate between the properties of conventional normal matrices and those of general matrices. In particular, the Schur form of an almost normal matrix can in a certain sense be considered canonical.

Key concepts: Normal matrix, Mathematics, Eigenvalues and eigenvectors, Matrix (chemical analysis), Pure mathematics, Square root of a 2 by 2 matrix, Orthogonal matrix, Combinatorics

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