In mathematics, the linear span (also called the linear hull or just span) of a set S {\displaystyle S} of elements of a vector space V {\displaystyle...

all linear combinations of these vectors. This set is called the linear span (or just span) of the vectors, say S = {v1, ..., vn}. We write the span of...

with linear span, but criteria for equality of k-spaces specified by sets of k vectors are not so simple. A dual description is provided with linear functionals...

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

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...

known as a spans Nebbiolo, an Italian wine grape also known as Span Linear span, or simply span, in linear algebra Span (category theory) <span>, an HTML...

intersection of linear subspaces is a linear subspace. Linear span Given a subset G of a vector space V, the linear span or simply the span of G is the smallest...

Least squares, linear least squares Gram–Schmidt process Woodbury matrix identity Vector space Linear combination Linear span Linear independence Scalar...

the right-hand vector is within that span. If every vector within that span has exactly one expression as a linear combination of the given left-hand vectors...

not generally a Hamel basis, since infinite linear combinations are required. Specifically, the linear span of the basis must be dense in H , {\displaystyle...

the direction of the affine span of X is also the linear span of the x – x0 for x in X. One says also that the affine span of X is generated by X and that...

are linearly independent and every element of V is a linear combination of elements of B. In other words, a basis is a linearly independent spanning set...

general sum of blades of arbitrary degree is called a multivector. The linear span of the k {\displaystyle k} -blades is called the k {\displaystyle k}...

\operatorname {Span} (Y)\}} by the inclusion order. In contrast, X {\displaystyle X} is linearly dependent if it has a proper subset whose span is a superset...

mdadm, or a device-spanning filesystem like btrfs; such volumes are usually called "spanned" or "linear | SPAN | BIG". A spanned volume provides no redundancy...

that is closed under these operations. It is often called the span (for example linear span) or the generated set. Let S be a set equipped with one or several...

In mathematics, the general linear group of degree n {\displaystyle n} is the set of n × n {\displaystyle n\times n} invertible matrices, together with...

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

space containing the points, exactly as the linear combinations of a set of vectors form their linear span. The affine combinations commute with any affine...

{\displaystyle X} is said to be a total subset of X {\displaystyle X} if the linear span of T {\displaystyle T} is a dense subset of X . {\displaystyle X.} This...

consisting of distinct points have a linear span in the canonical embedding with dimension directly related to that of the linear system in which they move; and...

linear subspace is the zero vector, for if S is any orthonormal set and v is orthogonal to S, then v is orthogonal to the closure of the linear span of...

In linear algebra, orthogonalization is the process of finding a set of orthogonal vectors that span a particular subspace. Formally, starting with a...

A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all...

procedure. Since the Franklin system has the same linear span as that of the Faber–Schauder system, this span is dense in C([0, 1]), hence in L2([0, 1]). The...

study concluded that attention span is not one singular linear equation; at age 15 it is recorded that attention-span-related abilities diverge. Over...

closure from topology is a closure operator. Other examples include the linear span of a subset of a vector space, the convex hull or affine hull of a subset...

volume of space, and so on. The linear span of a basis set B = {e1, e2, …, en} equals the position space R, denoted span(B) = R. Position vector fields...

combination one has a linear combination, and the resulting set is the linear span span ⁡ S {\displaystyle \operatorname {span} S} of S, which contains...