What is the difference between a correlation matrix and a covariance matrix?
A covariance matrix is a more generalized form of a simple correlation matrix.
Correlation is a scaled version of covariance; note that the two parameters always have the same sign (positive, negative, or 0). When the sign is positive, the variables are said to be positively correlated; when the sign is negative, the variables are said to be negatively correlated; and when the sign is 0, the variables are said to be uncorrelated.
Note also that correlation is dimensionless, since the numerator and denominator have the same physical units, namely the product of the units of
Best Linear Predictor
Our discussion here generalizes the one-dimensional case, when