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?
$\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.

3. Ah, very nice. Thank you sir.

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