Norm Definition and 263 Threads

can someone explain this proof please, I added a star to the inequalities I don't see/understand. if | | is a norm on a field K and if there is a C > 0 so that for all integers n |n.1| is smaller than or equal to C, the norm is non archimedean (ie the strong triangle inequality is true)...

Here's a question from Apostol's Calculus Vol1 Suppose that instead of the usual definition of norm of a vector in V_n, we define it the following way, ||A|| = \sum_{k=1}^{n}|a_k|. Using this definition in V_2 describe on a figure the set of all points (x,y) of norm 1. Is...

I don't know if I'm just having a slow day or what is going on but I am being stumped by this: If ||v|| = 2 and ||w|| = 3 what are the largest and smallest values possible for ||v - w||. Give a geometric explanation. Would it be as simple as just adding the two values for the largest, and...

Hi folks, I have to find the generalized solution for the following Ax=y : [1 2 3 4;0 -1 -2 2;0 0 0 1]x=[3;2;1] The rank of A is 3 so there is one nullity so the generalized solution is: X= x+alpha.n (where alpha is a constant , and n represents the nullity) I found the...

How does a norm differ from an absolute value? For example, is \|\mathbf{x}\| = \sqrt{x_1^2 + \cdots + x_n^2} any different than |\mathbf{x}| = \sqrt{x_1^2 + \cdots + x_n^2} ??

Show that the space c_0 of all sequences of real numbers that converge to 0 is a complete space with the l^\infty norm. First I let A^j=\{a_k^j\}_{k=1}^\infty be a sequence of sequences converging to zero and I assume that it is norm summable: \sum \limits_{j=1}^\infty ||A^j||_\infty <...

I'm having trouble with this for some reason. If A:\mathcal{H}\to \mathcal{H} is a bounded operator between Hilbert spaces, the norm of A is ||A|| = \inf\limits_{\psi \neq 0} \frac{||A\psi||}{||\psi||}. My trouble is in verifying that ||A|| is in fact a bound for A in the sense that...

I have this problem which I want to do before I go back to uni. The context was not covered in class before the break, but I want to get my head around the problem before we resume classes. So any help on this is greatly appreciated. Question Suppose C is a nonempty closed convex set in a...

Quickly can we define a hilbert space (H, <,>) where the vectors of this space have infinite norm? (i.e. the union of finite + infinite norm vectors form a complete space). If yes, can you give a link to a paper available on the web? If no, can you briefly describe why? Thanks in advance...

Are there names for the Lorentz invariant norm of the four-potential and four-current? I assume that they are invariant under the transformations. Also, is it true that any physical quantities which form a four-vector have an invariant quantity associated with them (i.e. the norm of the...

Hi, I have forgotten the formula for calculating the second norm of matrix. Does anyone know the formula? Regards, Niko

Hi I'm in the process of proving a matrix norm. The Frobenius norm is defined by an nxn matrix A by ||A||_F=sum[(|aij|^2)^(1/2) i=1..n,j=1..n] I'm having trouble showing ||A+B|| <= ||A|| + ||B|| thanks for the help

I am currently trying to norm an iq test. I would appreciate your participation. I am sure that you will find it interesting; go to: http://www.geocities.com/uiowa52405/iq.htm and click on logical iq test-the test is timed, for maximum time of 25 minutes.