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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
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 Just the norm? The norm acts on a vector and any norm has to satisfy three properties Given a vector space V over a field F, the norm must ‖x‖ ≥ 0 for all x and x = 0 ⇔ ‖x‖ = 0 ‖ax‖ = | a | ‖x‖ for all a ∈ F, x ∈ V ‖x + y‖ ≤ ‖x‖ + ‖y‖ (triangle inequality) You ask about the L1 and L2 norms The L1 norm is the sum of the absolute value of the entries in
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
1 and 2 norm inequality - Mathematics Stack Exchange where x ∈ Rn x ∈ R n There was no proof given, and I've been trying to prove it for a while now I know the definitions of the 1 1 and 2 2 norm, and, numerically the inequality seems obvious, although I don't know where to start rigorously Thank you
Norms on the reals - Mathematics Stack Exchange On the real numbers the absolute value is a norm on this vector space We can also define the norm of x x to be c|x| c | x |, where c> 0 c> 0 is a constant Are they the only norms on the real numbers? If not, what are other norms on the real numbers?