Use of the TOEPLITZ decomposition in the stratification of matrices

  • Adrián Ricardo Gómez Plata Universidad Militar Nueva Granada
Keywords: normal matrices, star shape, stratification

Abstract

Normal matrices N are a submanifold stratified in star shape R^(2n2) for practical purposes, it is convenient to know the details concerning the stratification of certain matrices. This article displays useful theorems that allow decanting a stratification of normal matrices using Toeplitz decomposition. The procedure will also facilitate the calculation of eigenvectors and eigenvalues using either Arnoldy or Lanczos Hermithian method according to Huthanen [4].

Author Biography

Adrián Ricardo Gómez Plata, Universidad Militar Nueva Granada
Matemático, Msc. Profesor Departamento de Matemáticas, Investigador Grupo Matrix. Universidad Militar Nueva Granada, Bogotá- Colombia.

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Author Biography

Adrián Ricardo Gómez Plata, Universidad Militar Nueva Granada
Matemático, Msc. Profesor Departamento de Matemáticas, Investigador Grupo Matrix. Universidad Militar Nueva Granada, Bogotá- Colombia.

References

BAKER A. (2001), Matrix Group. And Introduction to Lie Group Theory. Springer Undergraduate Mathematics Series.

GOMEZ, A (2005). A Strata of normal matrices. Ciencia e Ingeniería Neogranadina. 15: 6-11

HARD.R.M. (1975), Topological properties of subanalytic, sets, Trans.AMS, 211: 57-70

HUTHANEN.M. (2001). A Stratification of the set of normal matrices, SIAM J, Matrix Anal. Appl. Vol 23, N.2, pp 349-367

HORN.R., JOHNSON.C. (1985). Matrix Analysis. CAMBRIDGE UNIVERSITY PRESS.

MEYER.C. (2000), Matrix Análisis and Applied Linear Álgebra. SIAM.

PFLAUM.M. (2001). Analytic and Geometric Study of stratified spaces. Springer- Verlag Berlin Heidelberg: pg 15-53

POLLACK.A, GUILLEMIN.V. (2003), Topología diferencial UNAM.

SPIVAK.M. (1999), A Comprehensive introduction to Differential Geometry, Vol 1, Houston, Publish or Perish INC.

How to Cite
Gómez Plata, A. R. (2007). Use of the TOEPLITZ decomposition in the stratification of matrices. Ciencia E Ingenieria Neogranadina, 17(1), 5–12. https://doi.org/10.18359/rcin.1080
Published
2007-06-01
Section
ARTICLES

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