Linear algebra

In linear algebra, orthogonalization is the process of finding a set of orthogonal vectors that span a particular subspace. Formally, starting with a linearly independent set of vectors {v1, ... , vk} in an inner product space (most commonly the Euclidean space Rn), orthogonalization results in a set of orthogonal vectors {u1, ... , uk} that generate the same subspace as the vectors v1, ... , vk. Every vector in the new set is orthogonal to every other vector in the new set; and the new set and the old set have the same linear span.

square matrix without an inverse

set of equations with more equations than unknowns

matrix whose entries are the coefficients of a linear equation

transformation preserving the inner product

linear algebra operation

Mathematical map

theorem

In linear algebra, functional analysis and related areas of mathematics, a quasinorm is similar to a norm in that it satisfies the norm axioms, except that the triangle inequality is replaced by \|x + y\| \leq K(\|x\| + \|y\|) for some K > 1.

handedness of a vector space with ordered bases

Mathematical concept

affine subspace of an Euclidean space

category in mathematics

trace inequality between traces of exponential of symmetric matrices

elementary matrix representing a row-addition transformation

relation in algebra

basis of an algebraic structure that is canonical in a sense that depends on the precise context

formula computing the inverse of the sum of a matrix with the outer product of two vectors

frequency-domain analysis method

homomorphism between modules, paired with the associated homomorphism between the respective base rings

induced map between the dual spaces of the two vector spaces

inequality involving a real number and n-dimensional real vectors

describes in mathematics a linear transformation which converts the matrix into a column vector

Basis for v whose vectors are mutually orthogonal

inequality for real numbers

sequence satisfying a homogeneous linear recurrence with constant coefficients

process in linear algebra

study of matrices and their algebraic properties

Concept in linear algebra

Matrix form in linear algebra

non-diagonalizable matrix; one lacking a basis of eigenvectors

function over linear operators

In mathematics, the immanant of a matrix was defined by Dudley E. Littlewood and Archibald Read Richardson as a generalisation of the concepts of determinant and permanent.

method of solving linear programming problems, extending the simplex algorithm to problems with greater-than constraints by associating the constraints with large negative constants

tensor product space endowed with a special inner product