polynomial algebras are used for the study of algebraic varieties, which are solution sets of systems of polynomial equations. Weyl algebras and Lie algebras may...

linear operator contains information about the operator's eigenvalues. The minimal polynomial of an algebraic element records the simplest algebraic relation...

In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever...

article focuses on matrices related to linear algebra, and, unless otherwise specified, all matrices represent linear maps or may be viewed as such. Square...

generalizes the notion of Euclidean space. It extends the methods of linear algebra and calculus from the two-dimensional Euclidean plane and three-dimensional...

the algebraic representation of geometric concepts in n-dimensional space. Fearnley-Sander (1979) describes Grassmann's foundation of linear algebra as...

approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph...

In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors)...

Hogben, L, ed. (2007). Handbook of Linear Algebra.[page needed] Arthur, John W. (2011). Understanding Geometric Algebra for Electromagnetic Theory. IEEE...

theorem (linear algebra) Bregman–Minc inequality (discrete mathematics) Cauchy-Binet formula (linear algebra) Cayley–Hamilton theorem (Linear algebra) Dimension...

In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix into a rotation, followed by a rescaling followed...

Campbell, H: "Linear Algebra With Applications", pages 111–112. Appleton Century Crofts, 1971 Eves 1990, p. 405 A Brief History of Linear Algebra and Matrix...

6365. Nelson, Jelani; Nguyen, Huy L. (2013). OSNAP: Faster numerical linear algebra algorithms via sparser subspace embeddings. FOCS '13. arXiv:1211.1002...

In linear algebra, an invertible matrix is a square matrix that has an inverse. In other words, if some other matrix is multiplied by the invertible matrix...

geometry is a polarity that is a correlation of period 2. In linear algebra, an involution is a linear operator T on a vector space, such that T2 = I. Except...

Lipschutz, Seymour (2001), Schaum's outline of theory and problems of linear algebra, New York: McGraw-Hill, pp. 69–80, ISBN 978-0-07-136200-9 Press, WH;...

Numerical methods used in scientific computation, for example numerical linear algebra and numerical solution of partial differential equations Stochastic...

In linear algebra, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, major diagonal, or good diagonal) of a matrix A...

algorithm (incomplete) Basis (linear algebra) Burrows–Abadi–Needham logic Direct proof Generating a vector space Linear independence Polynomial Proof...

along with 4×4 matrix support. These are distinct from more general linear algebra libraries in other domains focussing on matrices of arbitrary size....

those transformations whose linear part has determinant 1 is the group of orientation- and volume-preserving maps. Algebraically, this group is a semidirect...

Springer-Verlag, ISBN 978-0-387-40510-0, MR 2014408. Lay, David (2003), Linear Algebra and Its Applications, Addison-Wesley, ISBN 978-0-201-70970-4. Mac Lane...

function fields. Algebraic structures occur as both discrete examples and continuous examples. Discrete algebras include: Boolean algebra used in logic gates...

environmental changes. In 1857, James Clerk Maxwell used the recently developed linear algebra to offer a mathematical proof of the Young–Helmholtz theory. The existence...

homological algebra, to construct long exact sequences. The snake lemma is valid in every abelian category and is a crucial tool in homological algebra and its...

MATLAB's initial linear algebra programming in 1967 with his one-time thesis advisor, George Forsythe. This was followed by Fortran code for linear equations...

formulas. Until the 19th century, algebra consisted mainly of the study of linear equations (presently linear algebra), and polynomial equations in a single...

irreducible, i.e., cannot be written as a product of two linear polynomials. Basic facts of abstract algebra then imply that the kernel of the above map is an...

rotations, linear momentum as the generator of translations, electric charge being the generator of the U(1) symmetry group of electromagnetism, the color charges...

theory). Continuous group theory, Lie algebras and differential geometry are used to understand the structure of linear and nonlinear partial differential...