Recent content by feryee

Yeah i see. Really great. But when it comes to plotting the plane by hand, wouldn't this becomes difficult to find all of such a vector on the plane?How can the plotting done in the easy/ handy way(not using software)

Thank you very much. That explains quiet well. Can you please tell me how can one claim that this equation actually represent a plane in ##\mathbb{R}^3##? If i get your explanations right , the choice of d will determine if we have a single plane or infinite family of parallel plane. right?

What exactly do you mean by convenient way? I couldn't still get it clearly? would you elaborate more on this!

why do we consider normal line in expressing a plane,say in ##R^3## ,of the form ## ax + by + cz = d ##? What is the logic behind this normal line selection? Plz provide intuitive explanations.Thanks

Thank you all for your comments. I finally proved it.

Well actually i have the final result but simply i couldn't get the same answer using geometric sum. Here is the final result: ##\frac{2\alpha}{(1+\alpha)(1-\alpha)^2}## How is it possible.

what is the result for the following double summation: ##\sum\limits_{i \neq j}^{\infty}\alpha^i\alpha^j ## where ## i, j =0,1,2,...##

No, This is an equation in a paper.(Eq 17 in ''New Steady-state analysis result for variable step-size LMS algorithm with different noise distributions'')

While reading a paper, i came across the following Expectations: Given that the ##E\left\{e^2_{n-i-1}e^2_{n-j-1}\right\}=E\left\{e^2_{n-i-1}\right\}E\left\{e^2_{n-j-1}\right\}## for ##i\neq j##.\\ Then as ##n\rightarrow\infty## ##E\left\{\left(\sum\limits_{i=0}^{n-2}\alpha^i...