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A vector space that is endowed with a norm.

A bilinear or sesquilinear form on a vector space generalising the dot product in Euclidean spaces.

In [[geometry]], a '''lattice''' is a discrete subgroup of a real [[vector space]].

...linear operator''') is a [[Function (mathematics)|function]] between two [[Vector space|vector spaces]] that preserves the operations of vector addition and [[Scal The term ''linear transformation'' is especially used for linear maps from a vector space to itself ([[Endomorphism|endomorphisms]]).

Vector space of all tangent vectors at a given point of a differentiable manifold.

...be labeled as 'vectors'. Thus, a vector is defined as a member of ''any'' vector space. Typical vector spaces include the real line, the Euclidean plane or space, ...ace is that superimposed vectors are again elements of the vector space (a vector space is closed under vector addition).

...ebraic structures such as a [[monoid]], [[group (mathematics)|group]] or [[vector space]] have a distinguished element, such as an [[identity element]], and [[morp ** [[Affine space]] versus [[vector space]];

...It is also a [[normed space]] since an inner product induces a norm on the vector space on which it is defined. A [[completeness|complete]] inner product space is

A ''Lie algebra'' is a vector space together with a skew-symmetric bilinear operation (the bracket) that fulfil

The property of a system of elements of a module or vector space, that no non-trivial linear combination is zero.

The set of all finite linear combinations of a module over a ring or a vector space over a field.

{{r|Vector space}}

{{r|Vector space}}

...nt space''' of a [[manifold_(geometry)|differentiable manifold]] M is a [[vector space]] at a point p on the manifold whose elements are the tangent vectors (or v ===Directional derivatives as a vector space===

...the minimal polynomial of a [[square matrix]], an [[endomorphism]] of a [[vector space]] or an [[algebraic number]]. ...y dependent]] since the matrix ring has dimension ''n''² as a [[vector space]] over ''F'', and so ''A'' satisfies some polynomial. Hence it makes sense

{{r|Vector space}}

...|groups]], [[ring (mathematics)|rings]], [[field (mathematics)|fields]], [[vector space]]s, and [[algebra over a field|algebras]].

In an [[affine space]] or [[vector space]] of [[dimension (vector space)|dimension]] ''n'' we take ''n''+1 points <math>s_0, s_1, \ldots, s_n</math

{{r|Dimension (vector space)}}

...is a [[division ring]], <math>M</math> is called a [[vector space/Advanced|vector space]]. While every nontrivial vector space has a basis, not every module over an arbitrary ring will have a basis. Th