# det(A+B) ?? det(A) + det(B)

• Sep 14th 2011, 08:01 AM
rubix
det(A+B) ?? det(A) + det(B)
I'm thinking
det(A+B) >= det(A) + det(B)

but I need a proof on this to formally prove something else.
• Sep 14th 2011, 08:45 AM
zoek
Re: det(A+B) ?? det(A) + det(B)
Quote:

Originally Posted by rubix
I'm thinking
det(A+B) >= det(A) + det(B)

but I need a proof on this to formally prove something else.

If $A=\left(\begin{array}{cc}1&0\\0&1\end{array}\right )$ and $B=\left(\begin{array}{cc}-1&0\\0&-1\end{array}\right)$ then $A+B = O$ so $det(A+B)= 0$

but $det(A) +det(B) = 1+1=2$.
• Sep 14th 2011, 09:57 AM
Ackbeet
Re: det(A+B) ?? det(A) + det(B)
Quote:

Originally Posted by rubix
I'm thinking
det(A+B) >= det(A) + det(B)

but I need a proof on this to formally prove something else.

As zoek has shown, your lemma is not true. What is the "something else" you're trying to prove?