If a vector space has dimension n, then any subset of n vectors that is linearly independent must be a basis, arbitrary vector space.

math.la.t.vsp.dim.linindep.arb


Basis theorem: for an n-dimensional vector space any linearly independent set with n elements is a basis, as is any spanning set with n elements; dimension of the column space of a matrix equals the number of pivot columns of the matrix; dimension of the null space of a matrix equals the number of free variables of the matrix

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August 25th, 2017
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