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
- 6 years ago
- Views
- 4
- Type
- Video
- Language
- English
- Content Type
- text/html; charset=utf-8

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
- 6 years ago
- Views
- 3
- Type
- Language
- English
- Content Type
- text/html