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Littlewood's algorithm and quaternion matrices

โœ Scribed by Dennis I. Merino; Vladimir V. Sergeichuk

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
137 KB
Volume
298
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

A strengthened form of Schur's triangularization theorem is given for quaternion matrices with real spectrum (for complex matrices it was given by Littlewood). It is used to classify projectors (A 2 = A) and self-annihilating operators (A 2 = 0) on a quaternion unitary space and examples of unitarily wild systems of operators on such a space are presented. Littlewood's algorithm for reducing a complex matrix to a canonical form under unitary similarity is extended to quaternion matrices whose eigenvalues have geometric multiplicity 1.

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