Math Help - symmetric matrix

1. symmetric matrix

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

2. 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}\$ $\
\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.

3. Ah, very nice. Thank you sir.

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