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- W4280497581 abstract "In this paper, we extend the definition of phases of sectorial matrices to those of semi-sectorial matrices, which are possibly singular. Properties of the phases are also extended, including those of the Moore-Penrose generalized inverse, compressions and Schur complements, matrix sums and products. In particular, a majorization relation is established between the phases of the nonzero eigenvalues of $AB$ and the phases of the compressions of $A$ and $B$, which leads to a generalized matrix small phase theorem. For the matrices which are not necessarily semi-sectorial, we define their (largest and smallest) essential phases via diagonal similarity transformation. An explicit expression for the essential phases of a Laplacian matrix of a directed graph is obtained." @default.
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- W4280497581 date "2022-04-29" @default.
- W4280497581 modified "2023-09-26" @default.
- W4280497581 title "On the Phases of a Semi-Sectorial Matrix" @default.
- W4280497581 doi "https://doi.org/10.48550/arxiv.2205.07607" @default.
- W4280497581 hasPublicationYear "2022" @default.
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