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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Spectral Theorems in Euclidean and Hermitian Spaces
verfasst von : Jean Gallier
Erschienen in: Geometric Methods and Applications
Verlag: Springer New York
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The goal of this chapter is to show that there are nice normal forms for symmetric matrices, skew-symmetric matrices, orthogonal matrices, and normal matrices. The spectral theorem for symmetric matrices states that symmetric matrices have real eigenvalues and that they can be diagonalized over an orthonormal basis. The spectral theorem for Hermitian matrices states that Hermitian matrices also have real eigenvalues and that they can be diagonalized over a complex orthonormal basis. Normal matrices can be block diagonalized over an orthonormal basis with blocks having size at most two, and there are refinements of this normal form for skewsymmetric and orthogonal matrices.