Hi MHF,
Consider 2 vectors x and m with the same dimension. Is the following condition true?
$\displaystyle (x - m)(x - m)^T == xx^T - mm^T$
It has been a while since I did linear algebra so some help is much appreciated!
That is exactly what I was thinking. Unfortunately problem I need to solve is this:
$\displaystyle S = \frac{1}{n-1}\sum\limits_{i=1}^n ({\bf x}_i - {\bf m})({\bf x}_i - {\bf m})^T$ where
$\displaystyle {\bf m} = \frac{1}{n}\sum\limits_{i=1}^n x_i$
Prove that the expression for the covariance matrix (above) can be rewritten as:
$\displaystyle S = \frac{(\sum\limits_{i=1}^n {\bf x}_i {\bf x}_i^T) - n {\bf m}{\bf m}^t }{n-1}$
I might have split the question wrong before. Anyone who sees now how you can rewrite the expression?