Covariance Matrix

The Covariance matrix is a matrix which contains the covariance for each possible combination of variables.

Let’s say we have a bidimensional dataset, then the covariance matrix will be:

$$\left[\begin{array}{ccc}\text{Cov}(x,x)& & \text{Cov}(x,y)\\ \text{Cov}(y,x)& & \text{Cov}(y,y)\end{array}\right]$$

Note that on the diagonal, we always have the covariance of a variable with itself, which is just the variance. In other words: $\text{Cov}(x,x)=\text{Var}(x)$.

Since the covariance has the commutative property (i.e. $\text{Cov}(x,y)=\text{Cov}(y,x)$), the covariance matrix is symmetric.

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statistics resources:

• Covariance Clearly Explained! - YouTube