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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2018, Volume 104, Issue 1, Pages 56–61 (Mi mz11667)

Solving Systems of Linear Equations with Normal Coefficient Matrices and the Degree of the Minimal Polyanalytic Polynomial

S. D. Ikramov

Lomonosov Moscow State University

Abstract: The generalized Lanczos process applied to a normal matrix $A$ builds up a condensed form of $A$, which can be described as a band matrix with slowly growing bandwidth. For certain classes of normal matrices, the bandwidth turns out to be constant. It is shown that, in such cases, the bandwidth is determined by the degree of the minimal polyanalytic polynomial of $A$. It was in relation to the generalized Lanczos process that M. Huhtanen introduced the concept of the minimal polyanalytic polynomial of a normal matrix.

Keywords: normal matrix, generalized Lanczos process, condensed form, band matrix, minimal polyanalytic polynomial.

DOI: https://doi.org/10.4213/mzm11667

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English version:
Mathematical Notes, 2018, 104:1, 48–52

Bibliographic databases:

UDC: 519.61
Revised: 23.11.2017

Citation: S. D. Ikramov, “Solving Systems of Linear Equations with Normal Coefficient Matrices and the Degree of the Minimal Polyanalytic Polynomial”, Mat. Zametki, 104:1 (2018), 56–61; Math. Notes, 104:1 (2018), 48–52

Citation in format AMSBIB
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