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Commutativity of (2 × 2) selfadjoint matrices

Published online by Cambridge University Press:  17 April 2009

W.J. Ricker
W.J. Ricker
Affiliation:
School of Mathematics, The University of NSW, PO Box 1 Kensington NSW 2033, Australia
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An elementary proof is given of the fact that an n–tuple A = (A1, …, An) of self-adjoint matrices in a 2-dimensional Hilbert space consists of mutually commuting matrices Aj, 1 ≤ j ≤ n, if and only if γ(A) is non-empty. Here γ(A) ⊆ ℝn is the joint spectrum of A (in the sense of McIntosh and Pryde) consisting of those points β ∈ ℝn for which the matrix is not invertible.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 2 , October 1993 , pp. 321 - 323
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Greiner, G. and Ricker, W.J., [Joint spectral sets and commutativity of systems of (2 × 2)selfadjoint matrices’, Linear and Multilinear Algebra (to appear).Google Scholar
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