Functional analysis Normed and Banach spaces Concept
Norm
Summary
A norm on a real or complex vector space is a function that gives each vector a length. It satisfies the triangle inequality and absolute homogeneity, and only the zero vector has length zero.
Where this leads
14 pages build on this one.
- Weak and strong extremum
- Normed algebra
- Kolmogorov's normability criterion
- Stability of a difference equation
- Hadamard's inequality in Fredholm theory
- Backward error analysis
- Hadamard's inequality
- Hadamard's maximal determinant problem
- Gowers norm
- Lyapunov exponent
- Numerical stability
- Banach algebra
- Matrix norm
- Bareiss algorithm
Further reading
About this page
| Tag | 0V2WP9B1MF |
|---|---|
| URI | m2://0V2WP9B1MF |
| Kind | concept |
| Writing | W1 stated |
| MSC | 46B20 |
| 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)
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What links here
Definitions
Special cases
Used by
- Weak and strong extremum
- Normed algebra
- Kolmogorov's normability criterion
- Stability of a difference equation
- Backward error analysis
- Hadamard's inequality
- Gowers norm
- Lyapunov exponent
- Numerical stability
- Matrix norm