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In mathematics, the dimension of a vector space V is the cardinality
(i.e. the number of vectors) of a basis of V over its base field.[1]

It is sometimes called Hamel dimension (after Georg Hamel) or
algebraic dimension to distinguish it from other types of dimension.

For every vector space there exists a basis,[a] and all bases of a vector space have equal cardinality;[b]
as a result, the dimension of a vector space is uniquely defined.
We say V is finite-dimensional if the dimension of V is finite, and infinite-dimensional if its dimension is infinite.

https://en.wikipedia.org/wiki/Dimension_(vector_space)

In mathematics, a set B of elements (vectors) in a vector space V is called a basis,
if every element of V may be written in a unique way as a (finite) linear combination of elements of B.
The coefficients of this linear combination are referred to as components or coordinates on B of the vector.
The elements of a basis are called basis vectors.

https://en.wikipedia.org/wiki/Basis_(linear_algebra)