The approximation of a totally positive band matrix by a strictly banded totally positive one
نویسندگان
چکیده
منابع مشابه
The 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 ...
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It is shown that a bounded bi-infinite banded totally positive matrix A is boundedly invertible iff there is one and only one bounded sequence mapped by A to the sequence ((-)')■ The argument shows that such a matrix has a main diagonal, i.e., the inverse of A is the bounded pointwise limit of inverses of finite sections of A principal with respect to a particular diagonal; hence ((—)'+^4~ (j, ...
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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...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1982
ISSN: 0024-3795
DOI: 10.1016/0024-3795(82)90139-2