An interlacing result for Hermitian matrices in Minkowski space

D. B. Janse van Rensburg; A. C.M. Ran; M. van Straaten

doi:10.1016/j.laa.2023.07.019

An interlacing result for Hermitian matrices in Minkowski space

D. B. Janse van Rensburg
, A. C.M. Ran^*
, M. van Straaten

^*Corresponding author for this work

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

In this paper we will look at the well known interlacing problem, but here we consider the result for Hermitian matrices in the Minkowski space, an indefinite inner product space with one negative square. More specific, we consider the n×n matrix A=[Ju−u^⁎a] with a∈R, J=J^⁎ and u∈Cⁿ⁻¹. Then A is H-selfadjoint with respect to the matrix H=I_n−1⊕(−1). The canonical form for the pair (A,H) plays an important role and the sign characteristic coupled to the pair is also discussed.

Original language	English
Pages (from-to)	236-247
Number of pages	12
Journal	Linear Algebra and its Applications
Volume	693
DOIs	https://doi.org/10.1016/j.laa.2023.07.019
Publication status	Published - 15 Jul 2024

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Publisher Copyright:
© 2023 The Author(s)

Keywords

Interlacing
Minkowski space

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10.1016/j.laa.2023.07.019

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title = "An interlacing result for Hermitian matrices in Minkowski space",

abstract = "In this paper we will look at the well known interlacing problem, but here we consider the result for Hermitian matrices in the Minkowski space, an indefinite inner product space with one negative square. More specific, we consider the n×n matrix A=[Ju−u⁎a] with a∈R, J=J⁎ and u∈Cn−1. Then A is H-selfadjoint with respect to the matrix H=In−1⊕(−1). The canonical form for the pair (A,H) plays an important role and the sign characteristic coupled to the pair is also discussed.",

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AU - Janse van Rensburg, D. B.

AU - Ran, A. C.M.

AU - van Straaten, M.

PY - 2024/7/15

Y1 - 2024/7/15

N2 - In this paper we will look at the well known interlacing problem, but here we consider the result for Hermitian matrices in the Minkowski space, an indefinite inner product space with one negative square. More specific, we consider the n×n matrix A=[Ju−u⁎a] with a∈R, J=J⁎ and u∈Cn−1. Then A is H-selfadjoint with respect to the matrix H=In−1⊕(−1). The canonical form for the pair (A,H) plays an important role and the sign characteristic coupled to the pair is also discussed.

AB - In this paper we will look at the well known interlacing problem, but here we consider the result for Hermitian matrices in the Minkowski space, an indefinite inner product space with one negative square. More specific, we consider the n×n matrix A=[Ju−u⁎a] with a∈R, J=J⁎ and u∈Cn−1. Then A is H-selfadjoint with respect to the matrix H=In−1⊕(−1). The canonical form for the pair (A,H) plays an important role and the sign characteristic coupled to the pair is also discussed.

KW - Interlacing

KW - Minkowski space

UR - https://www.scopus.com/pages/publications/85166929257

UR - https://www.scopus.com/pages/publications/85166929257#tab=citedBy

U2 - 10.1016/j.laa.2023.07.019

DO - 10.1016/j.laa.2023.07.019

M3 - Article

AN - SCOPUS:85166929257

SN - 0024-3795

VL - 693

SP - 236

EP - 247

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

An interlacing result for Hermitian matrices in Minkowski space

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