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basis
Sign in to saveAlso known as Hamel basis, algebraic basis, basis of a vector space, vector basis, base
subset of a vector space that allows defining coordinates
A basis is a minimal set of vectors in a vector space that can be combined together to create any other vector in that space, much like how a few basic ingredients can be mixed to make many different dishes. It matters because having a basis lets mathematicians and scientists assign coordinates to vectors, making it easier to perform calculations and understand the structure of complex mathematical spaces.
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The same vector (dark purple) can be represented in two different bases (purple and red arrows).
In mathematics, a set B of elements of a vector space V is called a basis (pl.: bases) if every element of V can 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 of the vector with respect to B. The elements of a basis are called basis vectors.