A compact normal operator ( in particular, a normal operator on a finite-dimensional linear space ) is unitarily diagonalizable.
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A compact normal operator ( in particular, a normal operator on a finite-dimensional linear space ) is unitarily diagonalizable.
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This implies the usual spectral theorem : every normal operator on a finite-dimensional space is diagonalizable by a unitary operator.
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The concept of normal matrices can be extended to normal operators on infinite dimensional Hilbert spaces and to normal elements in C *-algebras.
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Eigenvectors of a normal operator corresponding to different eigenvalues are orthogonal, and a normal operator stabilizes the orthogonal complement of each of its eigenspaces.
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Eigenvectors of a normal operator corresponding to different eigenvalues are orthogonal, and a normal operator stabilizes the orthogonal complement of each of its eigenspaces.
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The technical master may also be required to step in if the normal operator has encountered a problem, and does not know how to correct it.
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With stronger assumptions, when " T " is a normal operator acting on a Hilbert space, the domain of the functional calculus can be broadened.
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A normal operator has a representation A = B + i C where B, C are self-adjoint and commute, i . e . BC = CB.
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In the latter case, the Gelfand Naimark representation theorem is one avenue in the development of spectral theory for normal operators, and generalizes the notion of diagonalizing a normal matrix.
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