On the Subdifferentiability of Functions of a Matrix Spectrum I Mathematical F
On the Subdifferentiability of Functions of a Matrix Spectrum I Mathematical F
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The result of Lemma 1 extends immediately to general polynomials of the form (4). However, we shall not need to state this explicitly; instead we go on to consider the original matrix problem.
3 Eigenvalues of Matrices A matrix can be reduced via similarity transformations to a variety of canonical forms. A finite number of elementary unitary transformations is sufficient to reduce a matrix to Hessenberg form, where all subdiagonals except the first are reduced to zero; this can be further redu...ced to upper triangular or Schur form by a general unitary transformation. The spectrum of a matrix appears on the diagonal of its Schur form, but other information, such as invariant subspace information, is not apparent. In order to further reduce the matrix, i. E. To introduce zeros in the upper triangle as well as the lower, nonunitary transformations are generally required; such transformations are potentially quite ill-conditioned, i. E. The norm of the transformation times the norm of its inverse could be large.
What to read after On the Subdifferentiability of Functions of a Matrix Spectrum I Mathematical F?
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To quickly assess the difficulty of the text, read a short excerpt:
The result of Lemma 1 extends immediately to general polynomials of the form (4). However, we shall not need to state this explicitly; instead we go on to consider the original matrix problem.
3 Eigenvalues of Matrices A matrix can be reduced via similarity transformations to a variety of canonical forms. A finite number of elementary unitary transformations is sufficient to reduce a matrix to Hessenberg form, where all subdiagonals except the first are reduced to zero; this can be further redu...ced to upper triangular or Schur form by a general unitary transformation. The spectrum of a matrix appears on the diagonal of its Schur form, but other information, such as invariant subspace information, is not apparent. In order to further reduce the matrix, i. E. To introduce zeros in the upper triangle as well as the lower, nonunitary transformations are generally required; such transformations are potentially quite ill-conditioned, i. E. The norm of the transformation times the norm of its inverse could be large.
What to read after On the Subdifferentiability of Functions of a Matrix Spectrum I Mathematical F?
You can find similar books in the "Read Also" column, or choose other free books by James V Burke to read onlineMoreLess
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