On eigenvalues of rectangular matrices
| dc.creator | Borcea, Julius | |
| dc.creator | Shapiro, Boris | |
| dc.creator | Shapiro, Michael | |
| dc.date | 2007-11-22 | |
| dc.date.accessioned | 2026-07-07T08:44:35Z | |
| dc.date.available | 2026-07-07T08:44:35Z | |
| dc.description | 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 $\{\la_1,...,\la_k\}$ such that the linear combination $A+\la_1B_1+\la_2B_2+...+\la_kB_k$ has rank smaller than $m$ the {\it eigenvalue locus} of the latter pencil. Motivated primarily by applications to multi-parameter generalizations of the Heine-Stieltjes spectral problem, see \cite{He} and \cite{Vol}, we study a number of properties of the eigenvalue locus in the most important case $k=n-m+1$. | |
| dc.description | 10 pages, no figures, LaTeX2e | |
| dc.identifier | https://arxiv.org/abs/0711.3609 | |
| dc.identifier | http://arxiv.org/abs/0711.3609 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142706 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Representation Theory | |
| dc.subject | Spectral Theory | |
| dc.subject | Primary 15A18; Secondary 15A22 | |
| dc.title | On eigenvalues of rectangular matrices | |
| dc.type | text |