GENERALIZED MATRIX FUNCTIONS, IRREDUCIBILITY AND EQUALITY
نویسندگان
چکیده
منابع مشابه
Generalized matrix functions, determinant and permanent
In this paper, using permutation matrices or symmetric matrices, necessary and sufficient conditions are given for a generalized matrix function to be the determinant or the permanent. We prove that a generalized matrix function is the determinant or the permanent if and only if it preserves the product of symmetric permutation matrices. Also we show that a generalized matrix function is the de...
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We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Algebra, 1(2), 1973, pp. 163–171]. Our algorithms are based on Gaussian quadrature and Golub–Kahan bidiagonalization. Block variants are also investigated. Numerical experiments are performed to illustrate the effectiven...
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We find geometric and arithmetic conditions in order to characterize the irreducibility of the determinant of the generic Vandermonde matrix over the algebraic closure of any field k. We also characterize those determinants whose tropicalization with respect to the variables of a row is irreducible.
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We investigate an infinite class of polynomial sequences at(n; z) with integer parameter t 1, which reduce to the well-known Stern (diatomic) sequence when z = 1 and are (0, 1)-polynomials when t 2. These sequences are related to the theory of hyperbinary expansions. The main purpose of this paper is to obtain various irreducibility and factorization results, most of which involve cyclotomic po...
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We find geometric and arithmetic conditions on a finite set of integer exponents and the characteristic of a field k in order to characterize the irreducibility of the determinant of the generic Vandermonde matrix determined by these exponents in the algebraic closure of k. Tools from Tropical Geometry are then applied in order to characterize those determinants that are irreducible over any fi...
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ژورنال
عنوان ژورنال: Bulletin of the Korean Mathematical Society
سال: 2014
ISSN: 1015-8634
DOI: 10.4134/bkms.2014.51.6.1615