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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
How are $C^0,C^1$ norms defined - Mathematics Stack Exchange Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
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
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)
Definition of $L_\infty$ norm - Mathematics Stack Exchange Hence $\cup_{ p \ge 1 } B_p(0,1)$ is bounded, balanced, convex and contains $0$ in its interior, and so is the unit ball of some norm, in this case, $\|\cdot \|_\infty$ The point here is that there is a natural motivation in terms of the unit balls which 'converge' (in the above sense) to the $\|\cdot \|_\infty$ unit ball
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
linear algebra - How do I find the norm of a matrix? - Mathematics . . . I have the following matrix below and I would like to find the norm of the matrix I learned that the norm of a matrix is the square root of the maximum eigenvalue multiplied by the transpose of the matrix times the matrix Can anybody explain to me in further detail what steps I need to do after finding the maximum eigenvalue of the matrix below?
Intuitive explanation of $L^2$-norm - Mathematics Stack Exchange Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
Prove Operator Norm is a Norm on linear space [duplicate] Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers