Monday, March 3, 2014

Take screencast and ogv to Avi conversion in Ubuntu

For recording your screen, where we can demonstrate some videos or some functions, RecordMydesktop is a nice option in Ubuntu. It can be downloaded using Ubuntu Software Center. It is pretty easy to use too.

Here is the link for RecordMyDesktop:

However, this tool generates the video in ".ogv" format. If we wish to convert it into a commonly used format such as ".avi", we can use following commad:

$ mencoder input.ogv -ovc lavc -oac mp3lame -o output.avi


Saturday, March 1, 2014

Show that A^2 = 0 is possible but A’A = 0 is not possible (unless A= zero matrix).

Found a solution in Stackexchage and quoting it here:

if we put A=(aij)1i,jn , then At=(bij) , with bij=aji , so by definition:

If you now look at the main diagonal's general entry of the above, you get

So if AAt=0 then the above diagonal's entries are zero, but a sum of squared real numbers is zero iff each number is zero, so...