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Tr. Mat. Inst. Steklova, 2009, Volume 267, Pages 258–265 (Mi tm2592)  

This article is cited in 6 scientific papers (total in 6 papers)

On Eigenvalues of Rectangular Matrices

B. Shapiroa, M. Shapirob

a Department of Mathematics, Stockholm University, Stockholm, Sweden
b Department of Mathematics, Michigan State University, East Lansing, MI, USA

Abstract: Given a $(k+1)$-tuple $A,B_1,…,B_k$ of $m\times n$ matrices with $m\le n$, we call the set of all $k$-tuples of complex numbers $\{\lambda_1,…,\lambda_k\}$ such that the linear combination $A+\lambda_1B_1+\lambda_2B_2+…+\lambda_kB_k$ has rank smaller than $m$ the eigenvalue locus of the latter pencil. Motivated primarily by applications to multiparameter generalizations of the Heine–Stieltjes spectral problem, we study a number of properties of the eigenvalue locus in the most important case $k=n-m+1$.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2009, 267, 248–255

Bibliographic databases:

UDC: 512.643.5
Received in July 2008
Language:

Citation: B. Shapiro, M. Shapiro, “On Eigenvalues of Rectangular Matrices”, Singularities and applications, Collected papers, Tr. Mat. Inst. Steklova, 267, MAIK Nauka/Interperiodica, Moscow, 2009, 258–265; Proc. Steklov Inst. Math., 267 (2009), 248–255

Citation in format AMSBIB
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\paper On Eigenvalues of Rectangular Matrices
\inbook Singularities and applications
\bookinfo Collected papers
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\vol 267
\pages 258--265
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Shapiro B., “Algebro-geometric aspects of Heine-Stieltjes theory”, J. London Math. Soc. (2), 83:1 (2011), 36–56  crossref  mathscinet  zmath  isi  scopus
    2. Alexandersson P., Shapiro B., “Around a Multivariate Schmidt-Spitzer Theorem”, Linear Alg. Appl., 446 (2014), 356–368  crossref  mathscinet  zmath  isi  scopus
    3. M. A. Sokolov, “Generating functions of Chebyshev polynomials in three variables”, J. Math. Sci. (N. Y.), 213:5 (2016), 786–794  mathnet  crossref  mathscinet
    4. Damaskinsky E.V., Kulish P.P., Sokolov M.A., “on Calculation of Generating Functions of Chebyshev Polynomials in Several Variables”, J. Math. Phys., 56:6 (2015), 063507  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. Xu Yu., “Generalized Characteristic Polynomials and Gaussian Cubature Rules”, SIAM J. Matrix Anal. Appl., 36:3 (2015), 1129–1142  crossref  mathscinet  zmath  isi  scopus
    6. E. V. Damaskinsky, M. A. Sokolov, “The generating function of bivariate Chebyshev polynomials associated with the Lie algebra $G_2$”, Theoret. and Math. Phys., 192:2 (2017), 1115–1128  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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