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 ?
An ICMI study of linear algebra at university level, ref.
Shapiro offers a textbook for an intermediate upper-level undergraduate course in linear algebra that includes combinatorial matrix theory and graph theory.
Minimal prerequisites include background in linear algebra and elementary differential geometry.
We are delighted to be demonstrating with ClearSpeed to show that Mathematica can take advantage of the CSX600 Advance board's acceleration of dense linear algebra functions," says Roger Germundsson, Wolfram Research, director of research and development.
Introduction to Computational Linear Algebra (online access included)
The topics include ill-posed problems of linear algebra, integral geometry, linear problems for parabolic equations, and inverse coefficient problems for hyperbolic equations.
Penney (director, Mathematics/Statistics Actuarial Science Program, Purdue University) provides a unified introduction to undergraduate linear algebra, with applications to science, engineering, and computer science, offering analytical, algebraic, and geometric discussion of the provided definitions, theorems, and proofs.
the industry's only provider of automated flows from MATLAB(R) algorithms to silicon, has become the first company to provide a family of fixed-point linear algebra intellectual property (IP) cores for Xilinx FPGA devices.
They introduce quandle theory to readers who are comfortable with linear algebra and basic set theory but may have no previous exposure to abstract algebra, knot theory, or topology.
He alerts readers to what kind and level of mathematical skill is required to work out the various examples--trigonometry, calculus, high school algebra, or linear algebra.
The opening chapters offer an introduction to language, logic, and mathematics; subsequent coverage includes vector space, subspace, span, linear independence, basis, dimension, linear transformation, eigenvalue, and eigenvector, as well as elementary numerical methods and the computational problems of linear algebra.
The LabVIEW Embedded Development Module includes more than 400 analysis functions for signal processing, linear algebra, curve fitting, statistics and calculus.

Full browser ?