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pro vyhledávání: '"Arnold Richard Kräuter"'
Autor:
Arnold Richard Kräuter, Ik-Pyo Kim
Publikováno v:
Linear Algebra and its Applications. 537:100-117
We introduce the notion of dual matrices of an infinite matrix A, which are defined by the dual sequences of the rows of A and naturally connected to the Pascal matrix P = [ ( i j ) ] ( i , j = 0 , 1 , 2 , … ) . We present the Cholesky decompositio
Publikováno v:
Linear Algebra and its Applications. 281(1-3):259-263
Let A be a fully indecomposable, nonnegative matrix of order n with row sums r l , r n , and let s i equal the smallest positive element in row i of A . We prove the permanental inequality per (A)⩽ ∏ i=1 n s i + ∏ i=1 n (r i −s i ) and charac
Autor:
Suk-Geun Hwang, Arnold Richard Kräuter
Publikováno v:
Discrete Applied Mathematics. 84(1-3):133-144
Let A be a nonnegative integral n -square matrix with row sums r 1 , …, r n . It is known that per A ⩽ Π n i=1 r i ! l r i if A is a (0, 1)-matrix (Minc, 1963; Bregman, 1973) and also that per A ⩽ 1 + Π n i = 1 ( r i − 1) if A is fully inde
Autor:
Balder Ortner, Arnold Richard Kräuter
Publikováno v:
Linear Algebra and its Applications. 236:147-180
Sharp lower bounds for the determinant and the trace of a certain class of hermitian matrices are derived. Special attention is given to the discussion of the case of equality in these estimations. Since the trace turns out to be a special kind of co
Publikováno v:
Linear Algebra and its Applications. 373:1-3
Publikováno v:
Linear and Multilinear Algebra. 15:207-223
Let ω n denote the set of all n × n −(1, −1)-matrices. In [5] E. I. II. Wang posed the following problem. Is there a decent upper bound for [per A] when A ∊ ω n is nonsingular? In this paper we conjecture that the best possible bound is the
Publikováno v:
Linear and Multilinear Algebra. 13:311-322
A matrix A = (aij ) will be called convertible if there exists a matrix S(A) = (±aij ) such that per A = detS(A). P. M. Gibson [3] proved that a convertible n × n-(0, l)-matrix with positive permanent contains at least zeros. In this paper we consi
Publikováno v:
Israel Journal of Mathematics. 45:53-62
Let Ω n denote the set of alln×n-(1,−1)-matrices. E.T.H. Wang has posed the following problem: For eachn≧4, can one always find nonsingularA∈Ω n such that |perA|=|detA| (*)? We present a solution forn≦6 and, more generally, we show that (*
Autor:
Arnold Richard Kräuter
Publikováno v:
Linear and Multilinear Algebra. 20:367-371
Trying to reveal the actual origin of a theorem on the permanent of the sum of two matrices, we discovered a little known formula concerning the expansion of determinants by determinants of bordered matrices. In this note, we present a concise and se
Autor:
Arnold Richard Kräuter
Publikováno v:
Linear Algebra and its Applications. :39-55
The permanental spread of a complex square matrix A is defined to be the greatest distance between two roots of the equation per(zI − A) = 0. A preliminary study of this number as well as of two related quantities is given. In particular, we derive