The dimension of a subspace is less than or equal to the dimension of the whole space, arbitrary vector space.

math.la.t.vsp.subspace.dim.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
3 years ago
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Once the dimension of a vector space is known, then the determination of whether or not a set of vectors is linearly independent, or if it spans the vector space, can often be much easier. In this section we will state a workhorse theorem and then apply it to the column space and row space of a matrix. It will also help us describe a super-basis for \(\complex{m}\text{.}\)

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Submitted At
September 11th, 2017
 3 years ago
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