Jordan basis for an infinite-dimensional space
Large structures made of nowhere functions
We say that a real-valued function f defined on a positive Borel measure space (X,μ) is nowhere q-integrable if, for each nonvoid open subset U of X, the restriction is not in . When (X,μ) has some natural properties, we show that certain sets of functions defined in X which are p-integrable for some p’s but nowhere q-integrable for some other q’s (0 < p,q < ∞) admit a variety of large linear and algebraic structures within them. The presented results answer a question of Bernal-González,...
Line graphs: their maximum nullities and zero forcing numbers
The maximum nullity over a collection of matrices associated with a graph has been attracting the attention of numerous researchers for at least three decades. Along these lines various zero forcing parameters have been devised and utilized for bounding the maximum nullity. The maximum nullity and zero forcing number, and their positive counterparts, for general families of line graphs associated with graphs possessing a variety of specific properties are analysed. Building upon earlier work, where...
Lineability and algebrability of the set of holomorphic functions with a given domain of existence
We show that if U is a domain of existence in a separable Banach space, then the set of holomorphic functions on U whose domain of existence is U is lineable and algebrable.
Linear and -linear betweenness spaces
Linear dependence of zeros of polynomials and construction of primitve elements.
Linear extensions of relations between vector spaces
Let and be vector spaces over the same field . Following the terminology of Richard Arens [Pacific J. Math. 11 (1961), 9–23], a relation of into is called linear if and for all and . After improving and supplementing some former results on linear relations, we show that a relation of a linearly independent subset of into can be extended to a linear relation of into if and only if there exists a linear subspace of such that for all . Moreover, if generates...
Linear forms and axioms of choice
We work in set-theory without choice ZF. Given a commutative field , we consider the statement : “On every non null -vector space there exists a non-null linear form.” We investigate various statements which are equivalent to in ZF. Denoting by the two-element field, we deduce that implies the axiom of choice for pairs. We also deduce that implies the axiom of choice for linearly ordered sets isomorphic with .
Linear fractional transformations and companion matrices
Linear maps preserving rank 2 on the space of alternate matrices and their applications.
Linear operators preserving maximal column ranks of nonbinary boolean matrices
The maximal column rank of an m by n matrix is the maximal number of the columns of A which are linearly independent. We compare the maximal column rank with rank of matrices over a nonbinary Boolean algebra. We also characterize the linear operators which preserve the maximal column ranks of matrices over nonbinary Boolean algebra.
Linear operators that preserve Boolean rank of Boolean matrices
The Boolean rank of a nonzero Boolean matrix is the minimum number such that there exist an Boolean matrix and a Boolean matrix such that . In the previous research L. B. Beasley and N. J. Pullman obtained that a linear operator preserves Boolean rank if and only if it preserves Boolean ranks and . In this paper we extend this characterizations of linear operators that preserve the Boolean ranks of Boolean matrices. That is, we obtain that a linear operator preserves Boolean rank...
Linear Transformations Of Tensor Spaces Preserving Decomposable Vectors
Linear transformations of tensor spaces preserving decomposable vectors.
Lineare Algebra über Fastkörpern.
Lineare zweidimensionale Räume von stetigen Funktionen mit stetigen ersten Ableitungen
m-applications over finite fields
Matrices which commute with a given matrix upon a subspace
Matrix rank and inertia formulas in the analysis of general linear models
Matrix mathematics provides a powerful tool set for addressing statistical problems, in particular, the theory of matrix ranks and inertias has been developed as effective methodology of simplifying various complicated matrix expressions, and establishing equalities and inequalities occurred in statistical analysis. This paper describes how to establish exact formulas for calculating ranks and inertias of covariances of predictors and estimators of parameter spaces in general linear models (GLMs),...
Matrix rank certification.