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What is the norm of a complex number? [duplicate] In particular, this "algebraic norm" is not measuring distance, but rather measuring something about the multiplicative behavior of a + bi That it turns out to be the square of the geometric norm in this case is a deep geometric fact about the geometry of complex numbers
2-norm vs operator norm - Mathematics Stack Exchange The operator norm is a matrix operator norm associated with a vector norm It is defined as | | A | | OP = supx ≠ 0 Ax n x and different for each vector norm In case of the Euclidian norm | x | 2 the operator norm is equivalent to the 2-matrix norm (the maximum singular value, as you already stated) So every vector norm has an associated operator norm, for which sometimes simplified
matrices - What is this norm $\|A\|_*$ called and what is it . . . A similar asterisk notation is also used to represent the dual norm of a vector See page 637 of Boyd Vandenberghe's Convex Optimization See also Dual norm intuition The OP specifies that this is a matrix norm, but just providing some references in case anyone is as confused as I was about the notation overload
Understanding L1 and L2 norms - Mathematics Stack Exchange I am not a mathematics student but somehow have to know about L1 and L2 norms I am looking for some appropriate sources to learn these things and know they work and what are their differences I am
What is the difference between the Frobenius norm and the 2-norm of a . . . For example, in matlab, norm (A,2) gives you induced 2-norm, which they simply call the 2-norm So in that sense, the answer to your question is that the (induced) matrix 2-norm is ≤ than Frobenius norm, and the two are only equal when all of the matrix's eigenvalues have equal magnitude
1 and 2 norm inequality - Mathematics Stack Exchange where x ∈ Rn There was no proof given, and I've been trying to prove it for a while now I know the definitions of the 1 and 2 norm, and, numerically the inequality seems obvious, although I don't know where to start rigorously Thank you