# Classification of matrix subalgebras of length 1

## Related Articles

- Length computation of matrix subalgebras of special type. Markova, O. V. // Journal of Mathematical Sciences;Dec2008, Vol. 155 Issue 6, p908
Let {ie910-01} be a field and let {ie910-02} be a finite-dimensional {ie910-03}-algebra. We define the length of a finite generating set of this algebra as the smallest number k such that words of length not greater than k generate {ie910-04} as a vector space, and the length of the algebra is...

- Application of linear algebra in real life. Jixia Deng // Applied Mechanics & Materials;2014, Issue 556-562, p3392
Linear algebra is an important basic course in university mathematics, finite dimensional vector space and linear transformation theory mainly on matrix theory, and the combination of matrix. Concept in linear algebra is defined directly by the mathematical symbol, rarely by example to import....

- Reflections and Three-Dimensionality. Kolmykov, V. A. // Mathematical Notes;May/Jun2003, Vol. 73 Issue 5/6, p802
If the dimension of a linear space is not greater than $3$, then the characteristic polynomial of the Coxeter transformation associated with any symmetric matrix is invariant under the natural action of the symmetric group. If the dimensionality is greater than 3, then this statement...

- linear algebra Mathematics. // Dictionary of Theories;2002, p314
A definition of the term "linear algebra" is presented. It refers to the branch of algebra which is concerned with the study of vector spaces or more generally with modules over a ring. It outlines the study of matrices and systems of linear equations for being related with the origin of the term.

- LINEAR GROUPS WITH ALL SUBGROUPS PROFINITELY CLOSED. WEHRFRITZ, B. A. F. // Quarterly Journal of Mathematics;Jun2011, Vol. 62 Issue 2, p501
We characterize completely groups of matrices over commutative fields all of whose subgroups are closed in the profinite topology.

- CHARACTERISTICS OF (Î³, 3)-CRITICAL GRAPHS. Mojdeh, D. A.; Firoozi, P. // Applicable Analysis & Discrete Mathematics;Apr2010, Vol. 4 Issue 1, p197
In this note the (Î³, 3)-critical graphs are fairly classified. We show that a (Î³, 3 k)-critical graph is not necessarily a (Î³, 3 k')-critical for k â‰ 6= k and k; k' 2 Ïµ{1, 2, 3}. The (2, 3)-critical graphs are definitely characterized. Also the properties of (Î³,3)-critical...

- Long Bialgebras, Dimodule Algebras and Quantum Yangâ€“Baxter Modules over Long Bialgebras. Liang Zhang // Acta Mathematica Sinica;Jul2006, Vol. 22 Issue 4, p1261
This paper gives a sufficient and necessary condition for a bialgebra to be a Long bialgebra, and proves a braided product to be a Long bialgebra under some conditions. It also gives a direct sum decomposition of quantum Yangâ€“Baxter modules over Long bialgebras.

- New Order Relations in Set Optimization. Jahn, Johannes; Truong Xuan Duc Ha // Journal of Optimization Theory & Applications;Feb2011, Vol. 148 Issue 2, p209
In this paper we study a set optimization problem ( SOP), i.e. we minimize a set-valued objective map F, which takes values on a real linear space Y equipped with a pre-order induced by a convex cone K. We introduce new order relations on the power set $\mathcal{P}(Y)$ of Y (or on a subset of...

- Some Applications Of Semigroups And Computer Algebra In Discrete Structures. Bijev, G. // AIP Conference Proceedings;11/17/2009, Vol. 1184 Issue 1, p293
An algebraic approach to the pseudoinverse generalization problem in Boolean vector spaces is used. A map (p) is defined, which is similar to an orthogonal projection in linear vector spaces. Some other important maps with properties similar to those of the generalized inverses (pseudoinverses)...