nullity vector
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Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… … Wikipedia
Rank–nullity theorem — In mathematics, the rank–nullity theorem of linear algebra, in its simplest form, states that the rank and the nullity of a matrix add up to the number of columns of the matrix. Specifically, if A is an m by n matrix over the field F , then :rank … Wikipedia
Dimension (vector space) — In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V. It is sometimes called Hamel dimension or algebraic dimension to distinguish it from other types of dimension. This description… … Wikipedia
Dimension theorem for vector spaces — In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have equally many elements. This number of elements may be finite, or given by an infinite cardinal number, and defines the dimension of the space.… … Wikipedia
Linear map — In mathematics, a linear map, linear mapping, linear transformation, or linear operator (in some contexts also called linear function) is a function between two vector spaces that preserves the operations of vector addition and scalar… … Wikipedia
Rank (linear algebra) — The column rank of a matrix A is the maximum number of linearly independent column vectors of A. The row rank of a matrix A is the maximum number of linearly independent row vectors of A. Equivalently, the column rank of A is the dimension of the … Wikipedia
Kernel (matrix) — In linear algebra, the kernel or null space (also nullspace) of a matrix A is the set of all vectors x for which Ax = 0. The kernel of a matrix with n columns is a linear subspace of n dimensional Euclidean space.[1] The dimension… … Wikipedia
Matroid — In combinatorics, a branch of mathematics, a matroid ( /ˈmeɪ … Wikipedia
Column space — The column vectors of a matrix. In linear algebra, the column space of a matrix (sometimes called the range of a matrix) is the set of all possible linear combinations of its column vectors. The column space of an m × n matrix is a… … Wikipedia
List of linear algebra topics — This is a list of linear algebra topics. See also list of matrices glossary of tensor theory. Contents 1 Linear equations 2 Matrices 3 Matrix decompositions 4 … Wikipedia
Row space — In linear algebra, the row space of a matrix is the set of all possible linear combinations of its row vectors. The row space of an m times; n matrix is a subspace of n dimensional Euclidean space. The dimension of the row space is called the… … Wikipedia
