Remarks on condition numbers and optimally conditioned matrices
Matrix condition numbers are proved to be submultiplicative but neither subadditive nor superadditive, and the Frobenius and the default (based on the 2-norm) condition numbers are shown to be unitarily invariant. The equality of all the singular values of a square matrix is established as a necessa...
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oai:animorepository.dlsu.edu.ph:faculty_research-147082024-07-29T02:49:38Z Remarks on condition numbers and optimally conditioned matrices Estalilla, Aliento V. Pinpin, Lord Kenneth M. Matrix condition numbers are proved to be submultiplicative but neither subadditive nor superadditive, and the Frobenius and the default (based on the 2-norm) condition numbers are shown to be unitarily invariant. The equality of all the singular values of a square matrix is established as a necessary and sufficient condition for the matrix to be optimally conditioned under the 2-norm, making unitary, Hadamard and some diagonal and antidiagonal matrices possess unity condition numbers. 2005-03-01T08:00:00Z text https://animorepository.dlsu.edu.ph/faculty_research/12784 Faculty Research Work Animo Repository Matrices—Norms Numerical analysis Hadamard matrices Mathematics Numerical Analysis and Computation |
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De La Salle University |
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De La Salle University Library |
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Asia |
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Philippines Philippines |
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Matrices—Norms Numerical analysis Hadamard matrices Mathematics Numerical Analysis and Computation |
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Matrices—Norms Numerical analysis Hadamard matrices Mathematics Numerical Analysis and Computation Estalilla, Aliento V. Pinpin, Lord Kenneth M. Remarks on condition numbers and optimally conditioned matrices |
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Matrix condition numbers are proved to be submultiplicative but neither subadditive nor superadditive, and the Frobenius and the default (based on the 2-norm) condition numbers are shown to be unitarily invariant. The equality of all the singular values of a square matrix is established as a necessary and sufficient condition for the matrix to be optimally conditioned under the 2-norm, making unitary, Hadamard and some diagonal and antidiagonal matrices possess unity condition numbers. |
| format |
text |
| author |
Estalilla, Aliento V. Pinpin, Lord Kenneth M. |
| author_facet |
Estalilla, Aliento V. Pinpin, Lord Kenneth M. |
| author_sort |
Estalilla, Aliento V. |
| title |
Remarks on condition numbers and optimally conditioned matrices |
| title_short |
Remarks on condition numbers and optimally conditioned matrices |
| title_full |
Remarks on condition numbers and optimally conditioned matrices |
| title_fullStr |
Remarks on condition numbers and optimally conditioned matrices |
| title_full_unstemmed |
Remarks on condition numbers and optimally conditioned matrices |
| title_sort |
remarks on condition numbers and optimally conditioned matrices |
| publisher |
Animo Repository |
| publishDate |
2005 |
| url |
https://animorepository.dlsu.edu.ph/faculty_research/12784 |
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1806511035015757824 |