منابع مشابه
Totally Nonnegative (0, 1)-Matrices
We investigate (0, 1)-matrices which are totally nonnegative and therefore which have all of their eigenvalues equal to nonnegative real numbers. Such matrices are characterized by four forbidden submatrices (of orders 2 and 3). We show that the maximum number of 0s in an irreducible (0, 1)-matrix of order n is (n − 1) and characterize those matrices with this number of 0s. We also show that th...
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If/ is an irreducible character of Sn, these functions are known as immanants; if/ is an irreducible character of some subgroup G of Sn (extended trivially to all of Sn by defining /(vv) = 0 for w$G), these are known as generalized matrix functions. Note that the determinant and permanent are obtained by choosing / to be the sign character and trivial character of Sn, respectively. We should po...
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Is it possible to perform numerical linear algebra with structured matrices to high relative accuracy at a reasonable cost? In our talk we answer this question affirmatively for a class of structured matrices whose applications range from approximation theory to combinatorics to multivariate statistical analysis [1, 2, 4]—the Totally Nonnegative (TN) matrices, i.e. matrices all of whose minors ...
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Suppose λ1 ≥ · · · ≥ λn ≥ 0 are the eigenvalues of an n × n totally nonnegative matrix, and λ̃1 ≥ · · · ≥ λ̃k are the eigenvalues of a k × k principal submatrix. A short proof is given of the interlacing inequalities: λi ≥ λ̃i ≥ λi+n−k, i = 1, . . . , k. It is shown that if k = 1, 2, n− 2, n− 1, λi and λ̃j are nonnegative numbers satisfying the above inequalities, then there exists a totally nonneg...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1994
ISSN: 0024-3795
DOI: 10.1016/0024-3795(94)90350-6