Completely normal matrices |
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| Authors: | Michael D Sherman Ronald L Smith |
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| Institution: | 1. Dept of Mathematics, Notre Dame High School, 1400 Maple Ave, Elmira, NY 14904, United States;2. Dept of Mathematics, University of Tennessee at Chattanooga, 615 McCallie Ave, Chattanooga, TN 37403, United States |
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| Abstract: | Normal matrices in which all submatrices are normal are said to be completely normal. We characterize this class of matrices, determine the possible inertias of a particular completely normal matrix, and show that real matrices in this class are closed under (general) Schur complementation. We provide explicit formulas for the Moore–Penrose inverse of a completely normal matrix of size at least four. A result on irreducible principally normal matrices is derived as well. |
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| Keywords: | Normal matrices Completely normal matrices Principally normal matrices Irreducible matrices |
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