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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| Main Authors: | , |
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| Format: | text |
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Animo Repository
2005
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| Online Access: | https://animorepository.dlsu.edu.ph/faculty_research/12784 |
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| Institution: | De La Salle University |
| Summary: | 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. |
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