Linear Algebra

Also found in: Dictionary, Thesaurus, Acronyms, Wikipedia.
Related to Linear Algebra: matrix algebra

linear algebra

[′lin·ē·ər ′al·jə·brə]
The study of vector spaces and linear transformations.

Linear Algebra


the part of algebra that is most important for applications. The theory of linear equations was the first problem to arise that pertained to linear algebra. The development of the theory led to the creation of the theory of determinants and subsequently to the theory of matrices and the related theories of vector spaces and linear transformations in them. Linear algebra also encompasses the theory of forms, in particular quadratic forms, and, in part, the theory of invariants and the tensor calculus. Some branches of functional analysis constitute a further development of corresponding problems of linear algebra associated with the passage from n-dimensional vector spaces to infinite-dimensional linear spaces.


Aleksandrov, P. S. Lektsii po analiticheskoi geometrii .... Moscow, 1968.
Kurosh, A. G. Kurs vysshei algebry, 9th ed. Moscow, 1968.
Mal’tsev, A. I. Osnovy lineinoi algebry, 3rd ed. Moscow, 1970.
Faddeev, D. K., and V. N. Faddeeva. Vychislitel’nye metody lineinoi algebry, 2nd ed. Moscow-Leningrad, 1963.
References in periodicals archive ?
Zheng, On solutions of matrix equation AXB + CYD = F, Linear Algebra Appl.
Brestcher, Linear Algebra with Applications, Third edition, Pearson Prentice Hall, 2005.
In this light, it is hard to see that technique oriented computer technology is essential to the occurrence of the basic insights proper to elementary mathematics such as College Algebra and Linear Algebra.
Watkins, Linear maps that preserve commuting pairs of matrices, Linear Algebra Appl.
CULA offers performance up to a magnitude faster than highly optimized CPU-based linear algebra solvers.
An accessible introduction to the theoretical and computational aspects of linear algebra using Maple(TM)
0 users on SPARC systems and Pentium-based PCs can build faster applications with Rogue Wave's new Math Accelerator, which utilizes Basic Linear Algebra Subroutines, or BLAS.
Matousek started gathering these succinct applications of linear algebra some years ago, and has decided to share his collection with students.
Also, Prentice Hall has launched its MATLAB Curriculum Series, a selection of supplemental text for the following courses: digital signal processing, control theory, linear algebra, signals and systems.
Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines -- linear algebra, abstract algebra, and number theory -- into one comprehensive and fluid presentation, facilitating a deeper understanding of the topic and improving readers' retention of the main concepts.
Another is to make linear algebra comprehensive not just to math majors, but also to engineers and computer scientists who could find it very helpful, especially in computer graphics.
Case applications show how linear algebra is essential in solving problems involving differentiation equations, optimization, approximation, and combinatorics.

Full browser ?