Geodesic
On Eigenvalues of Rectangular Matrices
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Singularities and applications, Tome 267 (2009), pp. 258-265

Voir la notice de l'article provenant de la source Math-Net.Ru

Given a $(k+1)$-tuple $A,B_1,\dots,B_k$ of $m\times n$ matrices with $m\le n$, we call the set of all $k$-tuples of complex numbers $\{\lambda_1,\dots,\lambda_k\}$ such that the linear combination $A+\lambda_1B_1+\lambda_2B_2+\dots+\lambda_kB_k$ 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 $k=n-m+1$. 
@article{TM_2009_267_a19,
     author = {B. Shapiro and M. Shapiro},
     title = {On {Eigenvalues} of {Rectangular} {Matrices}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {258--265},
     publisher = {mathdoc},
     volume = {267},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2009_267_a19/}
}
TY  - JOUR
AU  - B. Shapiro
AU  - M. Shapiro
TI  - On Eigenvalues of Rectangular Matrices
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2009
SP  - 258
EP  - 265
VL  - 267
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2009_267_a19/
LA  - en
ID  - TM_2009_267_a19
ER  - 
%0 Journal Article
%A B. Shapiro
%A M. Shapiro
%T On Eigenvalues of Rectangular Matrices
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2009
%P 258-265
%V 267
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2009_267_a19/
%G en
%F TM_2009_267_a19
B. Shapiro; M. Shapiro. On Eigenvalues of Rectangular Matrices. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Singularities and applications, Tome 267 (2009), pp. 258-265. http://geodesic.mathdoc.fr/item/TM_2009_267_a19/