# symmetric matrix

• September 29th 2009, 11:21 PM
jut
symmetric matrix
Does multiplying a matrix by it’s transponse always results in a symmetric matrix?
• September 30th 2009, 12:14 AM
bram kierkels
Quote:

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.
• September 30th 2009, 01:15 AM
jut
Ah, very nice. Thank you sir. (Clapping)

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