Linear spanCyclic matricesFinite fieldsNecessary and sufficient conditions are given on matrices A, B and S, having entries in some field F and suitable dimensions, such that the linear span of the terms A(i)SB(i) over F is equal to the whole matrix space....
Our analysis is based on a weighted variant of Kasteleynʼs linear algebra technique.Previous article in issue Next article in issue Keywords Spanning cycle Perfect matching Kasteleynʼs theorem Triangulation Plane graph View PDFReferences [1] O. Aichholzer, T. Hackl, C. Huemer, F. ...
Two sets:VECTORS and SCALARS four operations: A VECTOR SPACE consists of: A set of objects called VECTORS with operation The vectors form a COMMUTATIVE. 1 1.3 © 2016 Pearson Education, Ltd. Linear Equations in Linear Algebra VECTOR EQUATIONS. REVIEW Linear Combinations Given vectors and given ...
- 《Linear Algebra & Its Applications》 被引量: 39发表: 1976年 Effective action for scalar fields in two-dimensional gravity We consider a general two-dimensional gravity model minimally or nonminimally coupled to a scalar field. The canonical form of the model is elucidated, and... MO ...
However, all of these sets will have the same number of vectors and will span the same space of R4. 5. What is the relationship between orthogonal vectors and linear independence? Orthogonal vectors are always linearly independent, but the reverse is not always true. If a set of vectors is...
Now, for each n\ge 1, the sets (K^\prime (n,m))_{n\le m\le 2n} are pairwise disjoint and their union satisfies \begin{aligned} \begin{aligned} \bigcup _{n\le m\le 2n} K^\prime (n,m)\subseteq \{u\in {{\,\mathrm {{\mathbb {Z}}}\,}}^4: u\in {\mathfrak {B}...
Linear Algebra & Its ApplicationsGiacomo Micheli, Joachim Rosenthal, Paolo Vettori, Linear spanning sets for matrix spaces. http://arxiv.org/abs/1409.3020G. Micheli, J. Rosenthal and P. Vettori, Linear spanning sets for matrix spaces, preprint, arXiv:1409.3020...
Linearly independent spanning sets and linear transformations for Multi-level EncryptionVector spaces-Linear transformations-Basis-CongruenceThe process of encryption plays a vital role for secure communication of data streams through unsecured channels. The concepts in modern algebra are met with a major ...
The Rado-Horn theorem provides necessary and sufficient conditions for when a collection of vectors can be partitioned into a fixed number of linearly independent sets. Such partitions exist if and only if every subset of the vectors satisfies the so-called Rado-Horn inequality. Today there are ...
Linear Algebra Appl. 458 (2014), 128–133. Article MathSciNet MATH Google Scholar Q. Liu, Y. Hong, H.-J. Lai: Edge-disjoint spanning trees and eigenvalues. Linear Algebra Appl. 444 (2014), 146–151. Article MathSciNet MATH Google Scholar H. Lu: Regular graphs, eigenvalues and ...