# Meaning of the covariance matrix?

I wonder about the excessive usage of the covariance matrix across all kinds of machine learning tools. So far, for me, the covariance is just a pre-step to get to the correlation. And as there is an obvious reason for the correlation itself, I wonder why I encounter the covariance so often. And, however, I wonder in general why it is used so much. What is/are the purposes for the covariance matrix?

• why "there is an obvious reason for the correlation itself" ? Jun 7 at 12:30
• The correlation has a purpose?
– Ben
Jun 7 at 12:40
• I don't understand - you are saying your question " there is an obvious reason for the correlation itself," - I wonder what differences between correlation and covariance makes it difficult ? Jun 7 at 13:19
• It is meant like: Is the correlation the only purpose for a covariance (matrix)? Or are there further purposes of the covariance (matrix)?
– Ben
Jun 7 at 13:34

In simple words: covariance matrix show the distribution magnitude and measure of directionalrelationship between variables for multivariate data in multidimensional space and useful tool for decorrelate variables or applied as transformation for other variables. Here is math-info cor and cov cor vs cov in ML space