Characterizations of rectangular totally and strictly totally positive matrices
نویسندگان
چکیده
منابع مشابه
An interlacing property of eigenvalues strictly totally positive matrices
We prove results concerning the interlacing of eigenvalues of principal submatrices of strictly totally positive (STP) matrices.
متن کاملAn Interlacing Property of Eigenvalues of Strictly Totally Positive Matrices
We prove results concerning the interlacing of eigenvalues of principal submatrices of strictly totally positive matrices. §
متن کاملSome Extremal Problems for Strictly Totally Positive Matrices
For a strictly totally positive M × N matrix A we show that the ratio IlAxllp/llxllp has exactly R = min{ M, N ) nonzero critical values for each fixed p ~ (1, ~ ) . Letting ~ denote the i th critical value, and x ~ an associated critical vector, we show that ~l > " " " > An > 0 and x i (unique up to multiplication by a constant) has exactly i 1 sign changes. These critical values are generaliz...
متن کاملThe Approximation of a Totally Positive Band Matrix by a Strictly Banded Totally Positive One*
Every nonsingular totally positive m-banded matrix is shown to be the product of m totally positive one-banded matrices and, therefore, the limit of strictly m-banded totally positive matrices. This result is then extended to (bi)infinite m-banded totally positive matrices with linearly independent rows and columns. In the process, such matrices are shown to possess at least one diagonal whose ...
متن کاملTotally Positive Density Matrices and Linear Preservers
The intersection between the set of totally nonnegative matrices, which are of interest in many areas of matrix theory and its applications, and the set of density matrices, which provide the mathematical description of quantum states, are investigated. The single qubit case is characterized, and several equivalent conditions for a quantum channel to preserve the set in that case are given. Hig...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2010
ISSN: 0024-3795
DOI: 10.1016/j.laa.2009.12.004