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- What is the norm of a complex number? [duplicate]
We can define the norm of a complex number in other ways, provided they satisfy the following properties Positive homogeneity Triangle inequality Zero norm iff zero vector We could define a $3$-norm where you sum up all the components cubed and take the cubic root The infinite norm simply takes the maximum component's absolute value as the
- What is the difference between the Frobenius norm and the 2-norm of a . . .
Frobenius norm = Element-wise 2-norm = Schatten 2-norm Induced 2-norm = Schatten $\infty$-norm This is also called Spectral norm So if by "2-norm" you mean element-wise or Schatten norm, then they are identical to Frobenius norm If you mean induced 2-norm, you get spectral 2-norm, which is $\le$ Frobenius norm (It should be less than or
- functional analysis - Sobolev space - norm $H^1$ and $H^1_0 . . .
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- Understanding L1 and L2 norms - Mathematics Stack Exchange
The L1 norm is the sum of the absolute value of the entries in the vector The L2 norm is the square root of the sum of the squares of entries of the vector In general, the Lp norm is the pth root of the sum of the entries of the vector raised to the pth power
- Inequalities in $l_p$ norm - Mathematics Stack Exchange
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- How are $C^0,C^1$ norms defined - Mathematics Stack Exchange
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- The Sub Differential of a Matrix $ {L}_{1} $ Norm
The use of $\|A\|_1$ to refer to the induced norm has been standard for a long time, and indeed I would suggest that the only reason the elementwise one-norm interpretation is popular today is because of the rise in low-rank approximation methods $\endgroup$ –
- matrices - Orthogonal matrix norm - Mathematics Stack Exchange
There are infinitely many norms that satisfy your requirements, and some of them are not invariant under right-multiplication of orthogonal matrix
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