We prove that semialgebraic sets of rectangular matrices of a fixed rank, of skew-symmetric matrices of a fixed rank and of real symmetric matrices whose eigenvalues have prescribed multiplicities are minimal submanifolds of the space of real matrices of a given size. (C) 2021 Elsevier Inc. All rights reserved.
On minimality of determinantal varieties / Kozhasov, Khazhgali. - In: LINEAR ALGEBRA AND ITS APPLICATIONS. - ISSN 0024-3795. - 626:(2021), pp. 56-78. [10.1016/j.laa.2021.05.011]
On minimality of determinantal varieties
Kozhasov, Khazhgali
2021-01-01
Abstract
We prove that semialgebraic sets of rectangular matrices of a fixed rank, of skew-symmetric matrices of a fixed rank and of real symmetric matrices whose eigenvalues have prescribed multiplicities are minimal submanifolds of the space of real matrices of a given size. (C) 2021 Elsevier Inc. All rights reserved.File in questo prodotto:
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