What is the term for E[x*y'] I know this is probably a very simple question, but I recall learning that for 2 random vectors, x & y,  with mean mx & my,
E[(x-mx)(y-my)'] is the covariance  &
E[xy'] is the correlation
However, according to wikipedia, the correlation is actually: 
E[(x-mx)*(y-my)']/(std(x)*std(y))
Thus, what is the correct term for: E[x*y']   (if such a term exists)
Thanks! 
 A: $\mathbb{E}(XY)$ is known as a joint moment or mixed moment of $X$ and $Y$.
The equivalent central moment $\mathbb{E}\big((X-\mu_X)(Y-\mu_Y)\big)$ is the covariance. This will be the same as $\mathbb{E}(XY)$ if the variables have been centered so that $\mu_X = \mu_Y = 0$.
The correlation of two variables is their covariance divided by the product of their standard deviations. If the variables have unit variance, so $\sigma_X = \sigma_Y = 1$, then their covariance is the same as their correlation.
If the variables have been standardised so they have mean zero and standard deviation one, then $\mathbb{E}(XY)$ is a simple formula for the correlation. This is one of the advantages of standardising your variables, if possible, before trying to prove something about their correlation.
A: The definition from wikipedia is correct. For $n$ dimensional random column vectors $x$ and $y$, the covariance matrix is n times n and it's $E[ (x-\mu_x)(y-\mu_y)^T ]$. If the means are zero, this equals $E[ xy^T ]$ and if the standard deviations are 1, this is also the correlation. 
In my experience, $E[ xy^T ]$ is usually of interest only because it is the covariance, ie because at least one mean is zero. 
A: So, after further research, I realized that there are indeed 2 definitions, depending on the field.
In statistics, the correlation is defined as: 
 $\frac{E[ (x-\mu_x)(y-\mu_y)^T]}{\sigma_x\sigma_y}$
In signal processing & random processes, correlation ussually means:
$E[x'y]$
As pointed out, the above quantity in statistics is refered to as the 'joint moment' or 'mixed moment'
Source: wikipedia:
http://en.wikipedia.org/wiki/Autocorrelation
