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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- GFDL-1.2
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- September 11th, 2017
- 4 years ago
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##### math.la.t.vsp.subspace.dim.equal