Find nilpotent

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• Nov 8th 2008, 11:57 AM
tttcomrader
Find nilpotent
Find two nilpotent 2 by 2 matrices such that their sum is not nilpotent.

I have been trying a few matrices but none are working, is there a more logical, easier way to find these matrices? thanks.
• Nov 8th 2008, 12:03 PM
clic-clac
01 00
00 10
are nilpotent, but their sum,
01
10
is inversible so it is not nilpotent :)
• Nov 8th 2008, 04:50 PM
tttcomrader
So inversible means no nilpotent? How so? Thanks.
• Nov 8th 2008, 05:10 PM
ThePerfectHacker
Quote:

Originally Posted by tttcomrader
So inversible means no nilpotent? How so? Thanks.

Because if \$\displaystyle A\$ is invertible then \$\displaystyle A^n\$ is invertible. Thus, if \$\displaystyle A^n\$ is not invertible then \$\displaystyle A\$ is not invertible. If \$\displaystyle A^n \$ is zero matrix then it means \$\displaystyle A^n\$ is not invertible and so \$\displaystyle A\$ is not invertible.
• Jan 27th 2009, 07:22 AM
arbolis
Quote:

Originally Posted by ThePerfectHacker
Because if \$\displaystyle A\$ is invertible then \$\displaystyle A^n\$ is invertible. Thus, if \$\displaystyle A^n\$ is not invertible then \$\displaystyle A\$ is not invertible. If \$\displaystyle A^n \$ is zero matrix then it means \$\displaystyle A^n\$ is not invertible and so \$\displaystyle A\$ is not invertible.

Thank you TPH, you just answered a question of mine. I'm glad I've searched into the forum.