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Chapter 14: Normal Matrices and the Spectral Theorem

Chapter 14: Normal Matrices and the Spectral Theorem

pp. 277-300

Authors

, Pomona College, California, , University of Utah
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Extract

Chapter 14: Every square complex matrix is unitarily similar to an upper triangular matrix, but which matrices are unitarily similar to a diagonal matrix? The answer is the main result of this chapter: the spectral theorem for normal matrices. Hermitian, skew-Hermitian, unitary, and circulant matrices are unitarily diagonalizable. As a consequence, they have special properties that we investigate in this and following chapters.

Keywords

  • Normal matrix
  • spectral theorem
  • commuting normal matrices
  • defect from normality
  • Fuglede–Putnam theorem
  • circulant matrices
  • Fourier matrix
  • Cartesian decomposition
  • symmetric normal matrix
  • symmetric unitary matrix
  • spectral projections
  • spectral resolution

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