Trace Invariance for Quaternion Matrices
Abstract
Let F be a f ield. It is a classical result in linear algebra that for each A, P ϵ Mn (F) such that P is nonsingular, tr A = tr (PAP-1). We show in this paper that the preceding property does not hold true if F is the division ring of real quaternions. We show that the only quaternion matrices that have their trace invariant under unitary similarity are Hermitian matrices, and that the only matrices that have their trace invariant under similarity are real scalar matrices.
Keywords: Trace, quaternion, unitary matrices, Hermitian matrices
LAYMAN’S ABSTRACT
We consider a classical result in linear algebra concerning the trace of
matrices with complex entries and we determine whether this result
holds true for the set of quaternion matrices.
Published
2015-12-15
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Section
Articles
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