a vector space V is called a basis (pl.: bases) if every element of V may 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, the trace of a square matrix A, denoted tr(A), is defined to be the sum of elements on the main diagonal (from the upper left to the...

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...

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...

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

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

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

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...

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, 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...

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

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

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...

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

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

-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...

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

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

In linear algebra, a frame of an inner product space is a generalization of a basis of a vector space to sets that may be linearly dependent. In the terminology...

This is a glossary of linear algebra. See also: glossary of module theory. Contents A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Affine transformation...

and classification of Lie groups in terms of Lie algebras, which are simpler objects of linear algebra. In more detail: for any Lie group, the multiplication...

variables. Linear algebra is a closely related field investigating variables that appear in several linear equations, called a system of linear equations...

cost of an asset Basis function Basis (linear algebra) Dual basis Orthonormal basis Schauder basis Basis (universal algebra) Basis of a matroid Generating...

number of vectors) of a basis of V over its base field. It is sometimes called Hamel dimension (after Georg Hamel) or algebraic dimension to distinguish...

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

In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of...

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...

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...