The concept of a dual norm arises in functional analysis, a branch of mathematics.
Let be a normed space (or, in a special case, a Banach space) over a number field (i.e. or ) with norm . Then the dual (or conjugate) normed space (another notation ) is defined as the set of all continuous linear functionals from into the base field . If is such a linear functional, then the dual norm of is defined by
1). Dual Norm of Vectors
If p, q ∈ satisfy , then the ℓp and ℓq norms are dual to each other.
For , the dual norm is with positive definite.
2). Dual Norm of Matrices
It is dual norm is
Singular value norm
- Kolmogorov, A.N.; Fomin, S.V. (1957), Elements of the Theory of Functions and Functional Analysis, Volume 1: Metric and Normed Spaces, Rochester: Graylock Press
- Rudin, Walter (1991), Functional analysis, McGraw-Hill Science, ISBN 978-0-07-054236-5
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