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Math Help - det(A+B) ?? det(A) + det(B)

  1. #1
    Junior Member rubix's Avatar
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    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.
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  2. #2
    Junior Member
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    Re: det(A+B) ?? det(A) + det(B)

    Quote Originally Posted by rubix View Post
    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.
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  3. #3
    A Plied Mathematician
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    Re: det(A+B) ?? det(A) + det(B)

    Quote Originally Posted by rubix View Post
    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?
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