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- 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
- 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
- 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 ‖ a x ‖ = | 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
- How are $C^0,C^1$ norms defined - Mathematics Stack Exchange
How are C0,C1 C 0, C 1 norms defined? I know Lp,L∞ L p, L ∞ norms but are the former defined
- 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
- normed spaces - The difference between $L_1$ and $L_2$ norm . . .
The 1 1 -norm and 2 2 -norm are both quite intuitive The 2 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
- L0 norm, L1 norm and L2 norm - Mathematics Stack Exchange
The L0 L 0 norm is the number of non-zero elements in a vector Then it is not strictly a measure of a distance, then you couln't say the equality directly implies a relation between ∥x∥1, ∥y∥1 ‖ x ‖ 1, ‖ y ‖ 1
- How do I find the norm of a matrix? - Mathematics Stack Exchange
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?
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