nLab
zero vector
Contents
Context
Linear algebra
linear algebra, higher linear algebra
Ingredients
Basic concepts

ring, A∞ ring

commutative ring, E∞ ring

module, ∞module, (∞,n)module

field, ∞field

vector space, 2vector space
rational vector space
real vector space
complex vector space

topological vector space

linear basis,
orthogonal basis, orthonormal basis

linear map, antilinear map

matrix (square, invertible, diagonal, hermitian, symmetric, …)

general linear group, matrix group

eigenspace, eigenvalue

inner product, Hermitian form
GramSchmidt process

Hilbert space
Theorems
(…)
Contents
Idea
Given a vector space $V \in Vect_\mathbb{K}$, its zero vector, denoted $0 \in V$, is the vector which is the neutral element of the underlying abelian group.
Even though the notation is the same, notice the difference to the zero element $0 \in \mathbb{K}$ of the ground field $\mathbb{K}$.
Last revised on April 18, 2024 at 03:50:18.
See the history of this page for a list of all contributions to it.