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

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...

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...

Basis of a matroid Basis of a linear program Coordinate system Change of basis – Coordinate change in linear algebra Frame of a vector space – Similar...

Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations...

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 (2015). Linear Algebra Done Right (PDF) (3rd ed.). Springer. ISBN 978-3-319-11079-0. Hefferon, Jim (2020). Linear Algebra (PDF) (4th ed.). Orthogonal...

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, 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...

Linear Algebra is a 1966 mathematics textbook by Serge Lang. The third edition of 1987 covers fundamental concepts of vector spaces, matrices, linear...

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

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

In mathematics, a linear algebraic group is a subgroup of the group of invertible n × n {\displaystyle n\times n} matrices (under matrix multiplication)...

Multilinear algebra is the study of functions with multiple vector-valued arguments, with the functions being linear maps with respect to each argument...

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

but also a direction. The concept of vector spaces is fundamental for linear algebra, together with the concept of matrices, which allows computing in vector...

homomorphism between two R-algebras is an R-linear ring homomorphism. Explicitly, φ : A1 → A2 is an associative algebra homomorphism if φ ( r ⋅ x ) = r ⋅ φ (...

55b). Previously, the official title was Honors Advanced Calculus and Linear Algebra. The course has gained reputation for its difficulty and accelerated...

glossary of linear algebra is a list of definitions and terms relevant to the field of linear algebra, the branch of mathematics concerned with linear equations...

-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...

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

For distinguishing such a linear function from the other concept, the term affine function is often used. In linear algebra, mathematical analysis, and...

conjugate transpose, and linear operators over a Hilbert space and Hermitian adjoints. However, it may happen that an algebra admits no involution. Look...

In linear algebra, the quotient of a vector space V {\displaystyle V} by a subspace U {\displaystyle U} is a vector space obtained by "collapsing" U {\displaystyle...

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

functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication...

Shilov, Linear Algebra (Trans. R. A. Silverman), Dover Publications, New York, 1977. Friedberg, Stephen; Insel, Arnold; Spence, Lawrence (2003). Linear Algebra...

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...