An alternative approach to unitoidness |
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Authors: | Donald W Robinson |
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Institution: | Department of Mathematics, Brigham Young University, Provo, UT 84602, USA |
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Abstract: | In a recent paper C.R. Johnson, S. Furtado, A generalization of Sylvester’s law of inertia, Linear Algebra Appl. 338 (2001) 287-290], Sylvester’s law of inertia is generalized to any matrix that is ∗-congruent to a diagonal matrix. Such a matrix is called unitoid. In the present paper, an alternative approach to the subject of unitoidness is offered. Specifically, Sylvester’s law of inertia states that a Hermitian n × n matrix of rank r with inertia (p, q, n − r) is ∗-congruent to the direct sum ei0Ip⊕eiπIq⊕0In-r. |
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Keywords: | 15A57 15A09 15A18 |
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