symmetric matrix

**jut** · September 29th 2009, 11:21 PM

Does multiplying a matrix by it’s transponse always results in a symmetric matrix?

**bram kierkels** · September 30th 2009, 12:14 AM

Originally Posted by jut

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.

**jut** · September 30th 2009, 01:15 AM

Ah, very nice. Thank you sir.

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

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