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...

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 linear algebra, the nonnegative rank of a nonnegative matrix is a concept similar to the usual linear rank of a real matrix, but adding the requirement...

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)...

-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...

Social position Social status Seniority Rank (differential topology) Rank (graph theory) Rank (linear algebra), the dimension of the vector space generated...

positive-definite Hermitian matrices. Sylvester’s inequality about the rank (linear algebra) of the product of two matrices. Sylvester's closed solution for...

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...

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, 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...

Calculating the rank of an expression can be done using rankof(expr) Rank (linear algebra), for a definition of rank as applied to matrices Rank (J programming...

mathematics, dimension of a ring Matroid rank – Maximum size of an independent set of the matroid Rank (linear algebra) – Dimension of the column space of...

definitions, as linear maps or more generally; and the rules for manipulations of tensors arise as an extension of linear algebra to multilinear algebra. In differential...

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

semisimple Lie algebra is a linear Lie algebra under the adjoint representation. This may lead to some ambiguity, as every Lie algebra is already linear with respect...

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

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

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

Robert E.; Plemmons, Robert J. (2003). "structured low-rank approximation". Linear Algebra and Its Applications. 366: 157–172. doi:10.1016/S0024-3795(02)00505-0...

linear groups, projective groups, Euclidean groups, etc. Many matrix groups are also algebraic. Other algebraic groups occur naturally in algebraic geometry...

In linear algebra, the column space (also called the range or image) of a matrix A is the span (set of all possible linear combinations) of its column...

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

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

Lie algebra of a maximal torus of the compact group. If g {\displaystyle {\mathfrak {g}}} is a linear Lie algebra (a Lie subalgebra of the Lie algebra of...

{\textstyle m\times n} matrix whose column rank is r {\textstyle r} . Therefore, there are r {\textstyle r} linearly independent columns in A {\textstyle A}...

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...

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...