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Displaying 101 – 120 of 206

Matrix rank/inertia formulas for least-squares solutions with statistical applications

Yongge Tian, Bo Jiang (2016)

Special Matrices

Least-Squares Solution (LSS) of a linear matrix equation and Ordinary Least-Squares Estimator (OLSE) of unknown parameters in a general linear model are two standard algebraical methods in computational mathematics and regression analysis. Assume that a symmetric quadratic matrix-valued function Φ(Z) = Q − ZPZ0 is given, where Z is taken as the LSS of the linear matrix equation AZ = B. In this paper, we establish a group of formulas for calculating maximum and minimum ranks and inertias of Φ(Z)...

Maximal column rank preservers of fuzzy matrices

Seok-Zun Song, Soo-Roh Park (2001)

Discussiones Mathematicae - General Algebra and Applications

This paper concerns two notions of rank of fuzzy matrices: maximal column rank and column rank. We investigate the difference of them. We also characterize the linear operators which preserve the maximal column rank of fuzzy matrices. That is, a linear operator T preserves maximal column rank if and only if it has the form T(X) = UXV with some invertible fuzzy matrices U and V.

Maximal nests of subspaces, the matrix Bruhat decomposition, and the marriage theorem---with an application to graph coloring.

Brualdi, Richard A. (2002)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Maximum rank of a power of a matrix of a given pattern

Svatopluk Poljak (1988)

Commentationes Mathematicae Universitatis Carolinae

Minimal $c p$ rank.

Shaked-Monderer, Naomi (2001)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Minimal sets of vectors which generate $R_{n}$ with excess $k$

Miroslav Fiedler (1979)

Czechoslovak Mathematical Journal

Minimum rank of edge subdivisions of graphs.

Barrett, Wayne, Bowcutt, Ryan, Cutler, Mark, Gibelyou, Seth, Owens, Kayla (2009)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Minimum rank of matrices described by a graph or pattern over the rational, real and complex numbers.

Berman, Avi, Friedland, Shmuel, Hogben, Leslie, Rothblum, Uriel G., Shader, Bryan (2008)

The Electronic Journal of Combinatorics [electronic only]

Minimum semidefinite rank of outerplanar graphs and the tree cover number.

Barioli, Francesco, Fallat, Shaun M., Mitchell, Lon H., Narayan, Sivaram K. (2011)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Mittelwertstrukturen.

Werner Bos (1972)

Mathematische Annalen

Multi-covering radius for rank metric codes.

Vasantha, W.B., Selvaraj, R.S. (2009)

The Electronic Journal of Combinatorics [electronic only]

N-Dimensional Binary Vector Spaces

Kenichi Arai, Hiroyuki Okazaki (2013)

Formalized Mathematics

The binary set {0, 1} together with modulo-2 addition and multiplication is called a binary field, which is denoted by F2. The binary field F2 is defined in [1]. A vector space over F2 is called a binary vector space. The set of all binary vectors of length n forms an n-dimensional vector space Vn over F2. Binary fields and n-dimensional binary vector spaces play an important role in practical computer science, for example, coding theory [15] and cryptology. In cryptology, binary fields and n-dimensional...

Nonsingularity and $P$ -matrices.

Jiří Rohn (1990)

Aplikace matematiky

New proofs of two previously published theorems relating nonsingularity of interval matrices to $P$ -matrices are given.

Note sur le rang d'une matrice

Dominik Szynal, Jan Szynal (1972)

Aplikace matematiky

On a group of mixed-type reverse-order laws for generalized inverses of a triple matrix product with applications.

Tian, Yongge, Liu, Yonghui (2007)

ELA. The Electronic Journal of Linear Algebra [electronic only]

On certain non-constructive properties of infinite-dimensional vector spaces

Eleftherios Tachtsis (2018)

Commentationes Mathematicae Universitatis Carolinae

In set theory without the axiom of choice ( $AC$ ), we study certain non-constructive properties of infinite-dimensional vector spaces. Among several results, we establish the following: (i) None of the principles AC $^{LO}$ (AC for linearly ordered families of nonempty sets)—and hence AC $^{WO}$ (AC for well-ordered families of nonempty sets)— $DC (< κ)$ (where $κ$ is an uncountable regular cardinal), and “for every infinite set $X$ , there is a bijection $f : X \to {0, 1} \times X$ ”, implies the statement “there exists a field $F$ such that every vector...

Currently displaying 101 – 120 of 206

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Displaying 101 – 120 of 206

Matrix rank/inertia formulas for least-squares solutions with statistical applications

Maximal column rank preservers of fuzzy matrices

Maximal nests of subspaces, the matrix Bruhat decomposition, and the marriage theorem---with an application to graph coloring.

Maximum rank of a power of a matrix of a given pattern

Minimal $c p$ rank.

Minimal sets of vectors which generate $R_{n}$ with excess $k$

Minimum rank of edge subdivisions of graphs.

Minimum rank of matrices described by a graph or pattern over the rational, real and complex numbers.

Minimum semidefinite rank of outerplanar graphs and the tree cover number.

Mittelwertstrukturen.

Multi-covering radius for rank metric codes.

N-Dimensional Binary Vector Spaces

Nonsingularity and $P$ -matrices.

Note sur le rang d'une matrice

On a group of mixed-type reverse-order laws for generalized inverses of a triple matrix product with applications.

On certain non-constructive properties of infinite-dimensional vector spaces

On generalized inverses of banded matrices.

On infinite bounded-Toeplitz extensions of Toeplitz matrices.

On Konieczny's conjecture of Boolean matrices.

On low rank perturbations of complex matrices and some discrete metric spaces.

Currently displaying 101 – 120 of 206