On the unitarily invariant norms and some related results
- 1 March 1987
- journal article
- research article
- Published by Taylor & Francis in Linear and Multilinear Algebra
- Vol. 20 (2) , 107-119
- https://doi.org/10.1080/03081088708817747
Abstract
A norm N defined on the linear space of n × n complex matrices (denoted by ) is said to be unitarily invariant if for any A in and n × n unitary matrix U. In this note we study the properties of unitarily invariant norms. Using the metric properties of with respect to this kind of norms, we characterize different classes of matrices such as normal, unitary. Hermitian, positive semi-definite matrices etc. Some approximation problems in are also investigated.Keywords
This publication has 7 references indexed in Scilit:
- The generalized spectral radius, numerical radius and spectral normLinear and Multilinear Algebra, 1984
- Unitarily invariant generalized matrix norms and hadamard productsLinear and Multilinear Algebra, 1984
- Finite-Dimensional Vector SpacesPublished by Springer Nature ,1974
- A theorem on the trace of certain matrix products and some applicationsJournal of Mathematical Psychology, 1970
- SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMSThe Quarterly Journal of Mathematics, 1960
- Some metric inequalities in the space of matricesProceedings of the American Mathematical Society, 1955
- Maximum Properties and Inequalities for the Eigenvalues of Completely Continuous OperatorsProceedings of the National Academy of Sciences, 1951