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On a Condensed Form for Normal Matrices under Finite Sequences of Elementary Unitary Similarities
| Content Provider | Semantic Scholar |
|---|---|
| Author | Elsner, Ludwig Ikramov, Kd |
| Copyright Year | 1997 |
| Abstract | Abstract It is generally known that any Hermitian matrix can be reduced to a tridiagonal form by a finite sequence of unitary similarities, namely Householder reflections. Recently A. Bunse-Gerstner and L. Elsner have found a condensed form to which any unitary matrix can be reduced, again by a finite sequence of Householder transformations. This condensed form can be considered as a pentadiagonal or block tridiagonal matrix with some additional zeros inside the band. We describe such a condensed form (or, more precisely, a set of such forms) for general normal matrices, where the number of nonzero elements does not exceed O(n 3 2 ) , n being the order of the normal matrix given. Two approaches to constructing the condensed form are outlined. The first approach is a geometrical Lanczos-type one where we use the so-called generalized Krylov sequences. The second, more constructive approach is an elimination process using Householder reflections. Our condensed form can be thought of as a variable-bandwidth form. An interesting feature of it is that for normal matrices whose spectra lie on algebraic curves of low degree the bandwidth is much smaller. |
| Starting Page | 79 |
| Ending Page | 98 |
| Page Count | 20 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/S0024-3795(96)00526-5 |
| Volume Number | 254 |
| Alternate Webpage(s) | http://www.mat.uniroma2.it/~tvmsscho/papers/ikramov_24sept.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/S0024-3795%2896%2900526-5 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
