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Math Help - symmetric matrix

  1. #1
    jut
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    symmetric matrix

    Does multiplying a matrix by itís transponse always results in a symmetric matrix?
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  2. #2
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    Quote Originally Posted by jut View Post
    Does multiplying a matrix by it’s transponse always results in a symmetric matrix?
    \begin{array}{cc}a&b\\c&d\end{array}\ \ <br />
\times\ \ \begin{array}{cc}a&c\\b&d\end{array}\ =\ \ \begin{array}{cc}a^2+b^2&ac+bd\\ca+db&c^2+d^2\end{  array}\ =\ \begin{array}{cc}a^2+b^2&ac+bd\\ac+bd&c^2+d^2\end{  array}
    Which is Symmetric
    You can do the same for larger matrices.
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  3. #3
    jut
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    Ah, very nice. Thank you sir.

    I suspected my answer was yes via some tests in MATLAB.
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