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

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...

of dimension ⁠ 2 × 3 {\displaystyle 2\times 3} ⁠. In linear algebra, matrices are used as linear maps. In geometry, matrices are used for geometric transformations...

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...

system is always linearly independent. Despite the name, an orthonormal basis is not, in general, a basis in the sense of linear algebra (Hamel basis)....

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

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

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...

λis are the eigenvalues of the matrix; they need not be distinct. In linear algebra, a Jordan normal form, also known as a Jordan canonical form, is an...

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

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...

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

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...

In linear algebra, a generalized eigenvector of an n × n {\displaystyle n\times n} matrix A {\displaystyle A} is a vector which satisfies certain criteria...

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

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

other linear-algebraic quantities give us useful information about a graph, for example about how well-connected it is, how well we can cluster or color the...

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

list of simple Lie groups can be used to read off the list of simple Lie algebras and Riemannian symmetric spaces. Together with the commutative Lie group...

laws, which aimed to describe color mixing algebraically. These laws laid the theoretical framework necessary for color experiments performed by Hermann...

new colors are linear combinations of the old colors. In short, the simplified language introduced before is not gauge invariant. Color charge is conserved...

has worked in various areas of algebra and symbolic computation, including Hilbert functions, Betti numbers, and linear programming. He has written a number...

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

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

Fearnley-Sander describes Grassmann's foundation of linear algebra as follows: The definition of a linear space (vector space) [...] became widely known around...

In linear algebra, an invertible matrix (non-singular, non-degenarate or regular) is a square matrix that has an inverse. In other words, if some other...

kernels to represent the data in a high dimensional feature space after which linear techniques such as support vector machines can be applied. Data represented...

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

In linear algebra, a branch of mathematics, the polarization identity is any one of a family of formulas that express the inner product of two vectors...

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;...