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1.
On some aspects of spectral theory for infinite bounded non-negative matrices in max algebra
Vladimir Müller, Aljoša Peperko, 2024, izvirni znanstveni članek

Povzetek: Several spectral radii formulas for infinite bounded non-negative matrices in max algebra are obtained. We also prove some Perron–Frobenius type results for such matrices. In particular, we obtain results on block triangular forms, which are similar to results on Frobenius normal form of $n \times n$ matrices. Some continuity results are also established.
Ključne besede: non-negative matrices, infinite bounded matrices, max algebra, Bonsall’s cone spectral radius, eigenvalues, continuity
Objavljeno v DiRROS: 30.05.2024; Ogledov: 114; Prenosov: 110
.pdf Celotno besedilo (1,77 MB)
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2.
Isotropy groups of the action of orthogonal $^\ast$congruence on Hermitian matrices
Tadej Starčič, 2024, izvirni znanstveni članek

Povzetek: We present a procedure which enables the computation and the description of structures of isotropy subgroups of the group of complex orthogonal matrices with respect to the action of $^\ast$congruence on Hermitian matrices. A key ingredient in our proof is an algorithm giving solutions of a certain rectangular block (complex-alternating) upper triangular Toeplitz matrix equation.
Ključne besede: isotropy groups, matrix equations, complex orthogonal matrices, Hermitian matrices, Toeplitz matrices
Objavljeno v DiRROS: 06.05.2024; Ogledov: 233; Prenosov: 140
.pdf Celotno besedilo (651,15 KB)
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3.
Isotropy groups of the action of orthogonal similarity on symmetric matrices
Tadej Starčič, 2023, izvirni znanstveni članek

Povzetek: We find an algorithmic procedure that enables the computation and description of the structure of the isotropy subgroups of the group of complex orthogonal matrices with respect to the action of similarity on complex symmetric matrices. A key step in our proof is to solve a certain rectangular block upper triangular Toeplitz matrix equation.
Ključne besede: isotropy groups, matrix equations, orthogonal matrices, symmetric matrices, Toeplitz matrices
Objavljeno v DiRROS: 08.04.2024; Ogledov: 237; Prenosov: 85
.pdf Celotno besedilo (2,08 MB)
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