On a condensed form for normal matrices under finite sequences of elementary unitary similarities

Elsner L, Ikramov KD (1997)
Linear Algebra and its Applications 254(1-3): 79-98.

Konferenzbeitrag | Veröffentlicht | Englisch
 
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Autor*in
Elsner, LudwigUniBi; Ikramov, Khakim D.
Abstract / Bemerkung
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 for, 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. (C) 1997 Elsevier Science Inc., 1997.
Erscheinungsjahr
1997
Band
254
Ausgabe
1-3
Seite(n)
79-98
Konferenz
5th Conference of the International Linear Algebra Society
Konferenzort
Atlanta, GA
Konferenzdatum
1995-08-16 – 1995-08-19
ISSN
0024-3795
Page URI
https://pub.uni-bielefeld.de/record/1637776

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Elsner L, Ikramov KD. On a condensed form for normal matrices under finite sequences of elementary unitary similarities. Linear Algebra and its Applications. 1997;254(1-3):79-98.
Elsner, L., & Ikramov, K. D. (1997). On a condensed form for normal matrices under finite sequences of elementary unitary similarities. Linear Algebra and its Applications, 254(1-3), 79-98. https://doi.org/10.1016/S0024-3795(96)00526-5
Elsner, L., and Ikramov, K. D. (1997). On a condensed form for normal matrices under finite sequences of elementary unitary similarities. Linear Algebra and its Applications 254, 79-98.
Elsner, L., & Ikramov, K.D., 1997. On a condensed form for normal matrices under finite sequences of elementary unitary similarities. Linear Algebra and its Applications, 254(1-3), p 79-98.
L. Elsner and K.D. Ikramov, “On a condensed form for normal matrices under finite sequences of elementary unitary similarities”, Linear Algebra and its Applications, vol. 254, 1997, pp. 79-98.
Elsner, L., Ikramov, K.D.: On a condensed form for normal matrices under finite sequences of elementary unitary similarities. Linear Algebra and its Applications. 254, 79-98 (1997).
Elsner, Ludwig, and Ikramov, Khakim D. “On a condensed form for normal matrices under finite sequences of elementary unitary similarities”. Linear Algebra and its Applications 254.1-3 (1997): 79-98.

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