vector space basis

A vector basis of a vector space V is defined as a subset v_1, ..., v_n of vectors in V that are linearly independent and span V. Consequently, if (v_1, v_2, ..., v_n) is a list of vectors in V, then these vectors form a vector basis if and only if every v element V can be uniquely written as v = a_1 v_1 + a_2 v_2 + ... + a_n v_n, where a_1, ..., a_n are elements of the base field.

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