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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 a + b i 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
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
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
The Sub Differential of a Matrix $ {L}_{1} $ Norm The use of ∥ ∥1 ‖ ‖ 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
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| | | A | | OP = sup x ≠ 0 A x n x and different for each vector norm In case of the Euclidian norm |x|2 | 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