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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We prove results concerning the interlacing of eigenvalues of principal submatrices of strictly totally positive (STP) matrices.
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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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We prove results concerning the interlacing of eigenvalues of principal submatrices of strictly totally positive matrices. §
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In order to represent, compute and reason with advanced data types one must go beyond the traditional treatment of data types as being inductive types and, instead, consider them as inductive families. Strictly positive types (SPTs) form a grammar for defining inductive types and, consequently, a fundamental question in the the theory of inductive families is what constitutes a corresponding gr...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1998
ISSN: 0021-9045
DOI: 10.1006/jath.1997.3132