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1
Content available remote

Two-level Cretan matrices constructed using SBIBD

100%
Balonin N. A., Seberry J.
Special Matrices
|
2015
|
tom 3
|
nr 1
EN
Two-level Cretan matrices are orthogonal matrices with two elements, x and y. At least one element per row and column is 1 and the other element has modulus ≤ 1. These have been studied in the Russian literature for applications in image processing and compression. Cretan matrices have been found by both mathematical and computational methods but this paper concentrates on mathematical solutions for the first time. We give, for the first time, families of Cretan matrices constructed using the incidence matrix of a symmetric balanced incomplete block design and Hadamard related difference sets.
2
Content available remote

Possible numbers ofx’s in an {x,y}-matrix with a given rank

81%
Ma C.
Open Mathematics
|
2017
|
tom 15
|
nr 1
974-977
EN
Let x, y be two distinct real numbers. An {x, y}-matrix is a matrix whose entries are either x or y. We determine the possible numbers of x’s in an {x, y}-matrix with a given rank. Our proof is constructive.
3
Content available remote

The Bruhat rank of a binary symmetric staircase pattern

61%
Du Z., da Fonseca C. M.
Open Mathematics
|
2016
|
tom 14
|
nr 1
832-840
EN
In this work we show that the Bruhat rank of a symmetric (0,1)-matrix of order n with a staircase pattern, total support, and containing In, is at most 2. Several other related questions are also discussed. Some illustrative examples are presented.
4
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Quotient of information matrices in comparison of linear experiments for quadratic estimation

61%
Stępniak C.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1599-1605
EN
The ordering of normal linear experiments with respect to quadratic estimation, introduced by Stępniak in [Ann. Inst. Statist. Math. A 49 (1997), 569-584], is extended here to the experiments involving the nuisance parameters. Typical experiments of this kind are induced by allocations of treatments in the blocks. Our main tool, called quotient of information matrices, may be interesting itself. It is known that any orthogonal allocation of treatments in blocks is optimal with respect to linear estimation of all treatment contrasts. We show that such allocation is, however, not optimal for quadratic estimation.
5
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A note on majorization transforms and Ryser’s algorithm

61%
Dahl G.
Special Matrices
|
2013
|
tom 1
17-24
EN
The notion of a transfer (or T -transform) is central in the theory of majorization. For instance, it lies behind the characterization of majorization in terms of doubly stochastic matrices. We introduce a new type of majorization transfer called L-transforms and prove some of its properties. Moreover, we discuss how L-transforms give a new perspective on Ryser’s algorithm for constructing (0; 1)-matrices with given row and column sums.
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