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The spectral theorem in quaternions. (English) Zbl 1030.15015

An exposition of the spectral theory of normal matrices with quaternion entries is presented. The principal objective of the paper is to set down detailed proofs of the quaternionic spectral theorem in both the matrix-theoretic and abstract formulations. A second objective of the paper is to unite and to reflect upon some related issues that are crucial to the study of linear algebra over the quaternions: spectra, modules, and inner products. A few applications of the spectral theorem, such as the polar and singular value decompositions, are also explained.

MSC:

15B33 Matrices over special rings (quaternions, finite fields, etc.)
15A18 Eigenvalues, singular values, and eigenvectors
15A21 Canonical forms, reductions, classification
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