منابع مشابه
Sparsiication of Rectangular Matrices
Given a rectangular matrix with more columns than rows, nd a base of linear combinations of the row vectors such that these contain as many zero entries as possible. This process is called \sparsiication" (of the matrix). A combinatorial search method to solve sparsiication is presented which needs exponentially many arithmetic operations (in terms of the size of the matrix). However, various p...
متن کاملPseudospectra of rectangular matrices
Pseudospectra of rectangular matrices vary continuously with the matrix entries, a feature that eigenvalues of these matrices do not have. Some properties of eigenvalues and pseudospectra of rectangular matrices are explored, and an efficient algorithm for the computation of pseudospectra is proposed. Applications are given in (square) eigenvalue computation (Lanczos iteration), square pseudosp...
متن کاملProducts of Random Rectangular Matrices
We study the asymptotic behaviour of points under matrix cocyles generated by rectangular matrices. In particular we prove a random Perron-Frobenius and a Multiplicative Ergodic Theorem. We also provide an example where such products of random rectangular matrices arise in the theory of random walks in random environments and where the Multiplicative Ergodic Theorem can be used to investigate r...
متن کاملRectangular random matrices, related convolution
We characterize asymptotic collective behavior of rectangular random matrices, the sizes of which tend to infinity at different rates. It appears that one can compute the limits of all noncommutative moments (thus all spectral properties) of the random matrices we consider because, when embedded in a space of larger square matrices, independent rectangular random matrices are asymptotically fre...
متن کاملOn Eigenvalues of Rectangular Matrices
Given a (k+1)-tuple A,B1, . . . , Bk of (m×n)-matrices withm ≤ n we call the set of all k-tuples of complex numbers {λ1, . . . , λk} such that the linear combination A + λ1B1 + λ2B2 + . . . + λkBk has rank smaller than m the eigenvalue locus of the latter pencil. Motivated primarily by applications to multi-parameter generalizations of the Heine-Stieltjes spectral problem, see [He] and [Vol], w...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1994
ISSN: 0024-3795
DOI: 10.1016/0024-3795(94)90314-x