Linear and multilinear algebra; matrix theory Systems of linear equations Concept
Rank of a matrix
Summary
The rank of a matrix is the dimension of the span of its columns, which equals the dimension of the span of its rows.
Where this leads
18 pages build on this one.
- Schoenberg's embedding criterion
- Determinantal variety
- Ordinary least squares
- Frisch–Waugh–Lovell theorem
- Kalman rank condition
- Kaczmarz method
- Hierarchical matrix
- Matrix completion
- Jacobian criterion
- Eckart–Young theorem
- Zermelo's navigation problem
- Instrumental variables estimation
- Determinantal ideal
- Linear regression
- Tensor rank
- Rank-one convexity
- Time-optimal control
- Drazin inverse
Further reading
- Web https://en.wikipedia.org/wiki/Rank_(linear_algebra), lead section
About this page
| Tag | 0ZC9YTXZRY |
|---|---|
| URI | m2://0ZC9YTXZRY |
| Kind | concept |
| Writing | W1 stated |
| MSC | 15A03 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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What links here
Definitions
Used by
- Schoenberg's embedding criterion
- Determinantal variety
- Ordinary least squares
- Frisch–Waugh–Lovell theorem
- Kalman rank condition
- Kaczmarz method
- Hierarchical matrix
- Matrix completion
- Jacobian criterion
- Eckart–Young theorem
- Instrumental variables estimation
- Determinantal ideal
- Linear regression
- Tensor rank
- Rank-one convexity
- Drazin inverse