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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
- 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
- How are $C^0,C^1$ norms defined - Mathematics Stack Exchange
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- linear algebra - 2-norm vs operator norm - Mathematics Stack Exchange
So every vector norm has an associated operator norm, for which sometimes simplified expressions as exist The Frobenius norm (i e the sum of singular values) is a matrix norm (it fulfills the norm axioms), but not an operator norm, since no vector norm exists so that the above definition for the operator norm matches the Frobenius norm
- What is the reason norm properties are defined the way they are?
The intuition behind the definition of norm is that the norm of a vector is a way to measure the length of the vector Then the definition becomes clear: The length should be non-negative In a triangle, the length of one side is smaller than the sum of the lengths of the other sides (this where the name triangle inequality comes from)
- Intuitive explanation of $L^2$-norm - Mathematics Stack Exchange
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- What are some usual norms for matrices?
Norms ("just" a norm): Sometimes a norm is just a norm Often, it's useful to think of a matrix as "a box of numbers" in the same way that you would think of a vector in $\Bbb R^n$ as a "list of numbers"
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