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Isometries of the Vector p-Norms: Signed and Complex Permutation Matrices
Recall that in linear algebra, the vector p-norm of a vector x ∈ Cn (or x ∈ Rn) is defined to be where xi is the ith element of x and 1 ≤ p ≤ ∞ (where the p = ∞ case is understood to mean the limit as...
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MATLAB Scripts for Computing Completely Bounded Norms via Semidefinite...
In operator theory, the completely bounded norm of a linear map on complex matrices is defined by , where is the usual norm on linear maps defined by and is the operator norm of [1]. The completely...
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Norms and Dual Norms as Supremums and Infimums
Let be a finite-dimensional Hilbert space over or (the fields of real and complex numbers, respectively). If we let be a norm on (not necessarily the norm induced by the inner product), then the dual...
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How to compute hard-to-compute matrix norms
There are a wide variety of different norms of matrices and operators that are useful in many different contexts. Some matrix norms, such as the Schatten norms and Ky Fan norms, are easy to compute...
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