Kernel Definition and 211 Threads

This is probably a simple question, but just to be sure: if the kernel of linear transformation is {0}, then the set is linearly dependent since 0-vector is LD, right? So dimension is 0, right? Then what's the basis of kernel? No basis? thanks in advance.

If you have the following kernel (I think that's what it's called): A-\lambda I=\begin{pmatrix}4 & 1 \\ 4 & 1\end{pmatrix} You could write the eigenvector as: \operatorname{span}\begin{pmatrix}1 \\ -4\end{pmatrix} My question is: does it matter how you write the "span" part of it...

hi, i got a algebra question regarding kernel 1.what is the kernel of intergration operator: T(p)= p'(x)? 2. what is the kernel of differentiation operator : T(p) = integration of p(x) from -1 to 1 thanks

I've recently noticed that there is a 'Show Kernel Times' option in Windows XP's Task Manager under the 'Performance' tab. This shows up as a red meter over the green 'CPU Usage' meter. I gathered that the Kernel is a piece of software that allows the operating system to multi-task but what...

First the problem: If D_n is the Dirichlet kernel, I need to show that there exist positive constants c_1 and c_2 such that c_1 \log n \le \int\limits_{ - \pi }^\pi {\left| {D_n \left( t \right)} \right|dt} \le c_2 \log n for n=2,3,4,.... The only thing I have been able to do is this...

Show that the kernel of a field homomorphism is either the trivial homomorphism or isomorphic to the field. I've tried to see it as a factor group, but I'm stuck. Can someone help? mary

Hello i would need help to solve the integral equation with Kernel K(st)...

Hi, What's the relationship between the image and kernel of T and the image and kernel of Tn? I think we saw in class something along the lines of: Ker(T) \subseteq Ker(T^2) Im(T) \supseteq Im(T^2) My intuition is that this is also correct for any natural n, but is it true and if so...

Hi, does anyone know how to figure out the kernal and range for this linear transformation from P3 into P3 : L(p(x)) = xp'(x)? I thought ker(L)= {0} and range is P3. But the correct answer is ker (L) = P1, L(P3) = Span (x^2, x). Can someone explain to me how exactly do we fine the kernel and...

This thread is my point of view on us as Self-Award-Complex-Systems (SACS), which are part of their universe, therefore active participators in it. I think that one of the most important properties of SACS is their ability to associate between opposite things in non-destructive ways. The...

[SOLVED] Linux kernel module support How is it these days? IMO this is one of major areas where Linux used to lag behind Windows. Loading/unloading modules during runtime was not always reliable and sort of a pain... has it been improved in the last year or two?