a vector space V is called a basis (pl.: bases) if every element of V can be written in a unique way as a finite linear combination of elements of B....

Linear algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b...

In linear algebra, two n-by-n matrices A and B are called similar if there exists an invertible n-by-n matrix P such that B = P − 1 A P . {\displaystyle...

In linear algebra, the trace of a square matrix A, denoted tr(A), is the sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle...

In linear algebra and functional analysis, a projection is a linear transformation P {\displaystyle P} from a vector space to itself (an endomorphism)...

Sheldon Jay (1997), Linear Algebra Done Right (2nd ed.), Springer-Verlag, ISBN 0-387-98259-0. Lay, David C. (2005), Linear Algebra and Its Applications...

specifically in linear algebra, a linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is...

In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal number...

mathematics, particularly linear algebra, an orthonormal basis for an inner product space V {\displaystyle V} with finite dimension is a basis for V {\displaystyle...

Basis set may refer to: Basis (linear algebra) Basis set (chemistry) This disambiguation page lists articles associated with the title Basis set. If an...

is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector...

In mathematics, particularly linear algebra, an orthogonal basis for an inner product space V {\displaystyle V} is a basis for V {\displaystyle V} whose...

Hilbert space. A basis of a Hilbert space is not the same thing as a basis of a linear algebra. For distinction, a linear algebra basis for a Hilbert space...

forms a basis for L2[0,1]. Basis (linear algebra) (Hamel basis) Schauder basis (in a Banach space) Dual basis Biorthogonal system (Markushevich basis) Orthonormal...

The rank–nullity theorem is a theorem in linear algebra, which asserts: the number of columns of a matrix M is the sum of the rank of M and the nullity...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

org. Sanderson, Grant (August 6, 2016). "Linear combinations, span, and basis vectors". Essence of Linear Algebra. Archived from the original on 2021-12-11...

Evar D. (1970), Linear Algebra and Matrix Theory (2nd ed.), New York: Wiley, LCCN 76091646 MIT Linear Algebra Lecture on Change of Basis, from MIT OpenCourseWare...

the algebraic dual space. When defined for a topological vector space, there is a subspace of the dual space, corresponding to continuous linear functionals...

exist two such two-dimensional algebras. Each algebra consists of linear combinations (with complex coefficients) of two basis elements, 1 (the identity element)...

In linear algebra, a minor of a matrix A is the determinant of some smaller square matrix generated from A by removing one or more of its rows and columns...

In mathematics, particularly in linear algebra, a flag is an increasing sequence of subspaces of a finite-dimensional vector space V. Here "increasing"...

specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function)...

variables. Linear algebra is a closely related field that investigates linear equations and combinations of them called systems of linear equations. It...

Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which...

finite extension fields, it means the polynomial basis. In linear algebra, it refers to a set of n linearly independent generalized eigenvectors of an n×n...

-2),} since it makes all three equations valid. Linear systems are a fundamental part of linear algebra, a subject used in most modern mathematics. Computational...

resulting algebraic structure is a monoid, usually called the full linear monoid, but occasionally also full linear semigroup, general linear monoid etc...

abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures...

mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure...