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

- Created On
- August 25th, 2017
- 7 years ago
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- 4
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- Video
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- English
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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 \(\complex{m}\text{.}\)

- License
- GFDL-1.2
- Submitted At
- September 11th, 2017
- 7 years ago
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- 3
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- Language
- English
- Content Type
- text/html