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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 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
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
What are some usual norms for matrices? - Mathematics Stack Exchange The Frobenius norm falls into the class of matrix norms that are unitarily invariant, that is, norms ‖ ⋅ ‖ that satisfy ‖UAV‖ = ‖A‖ for compatible unitary matrices U, V Equivalently, these are the matrix norms that can be expressed as the result of a vector norm applied to the vector of singular values (cf Bhatia's Matrix Analysis)
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?
normed spaces - The difference between $L_1$ and $L_2$ norm . . . The 1 -norm and 2 -norm are both quite intuitive The 2 -norm is the usual notion of straight-line distance, or distance ‘as the crow flies’: it’s the length of a straight line segment joining the two points