TY - JOUR
T1 - An interlacing result for Hermitian matrices in Minkowski space
AU - Janse van Rensburg, D. B.
AU - Ran, A. C.M.
AU - van Straaten, M.
N1 - Publisher Copyright:
© 2023 The Author(s)
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
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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 -