Does multiplying a matrix by it’s transponsealwaysresults in a symmetric matrix?

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- Sep 29th 2009, 11:21 PMjutsymmetric matrix
Does multiplying a matrix by it’s transponse

*always*results in a symmetric matrix? - Sep 30th 2009, 12:14 AMbram kierkels
$\displaystyle \begin{array}{cc}a&b\\c&d\end{array}\ $$\displaystyle \

\times\ $$\displaystyle \ \begin{array}{cc}a&c\\b&d\end{array}\ =\ $$\displaystyle \ \begin{array}{cc}a^2+b^2&ac+bd\\ca+db&c^2+d^2\end{ array}\ $$\displaystyle =\ \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. - Sep 30th 2009, 01:15 AMjut
Ah, very nice. Thank you sir. (Clapping)

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