# Variance from the covariance matrix

I was reading about Common Spatial Pattern.

The CSP algorithm tries to find the vector $$w^T$$ that maximises the ratio of variance between two windows $$X_1$$ of size $$(n,t_1)$$ and $$X_2$$ of size $$(n,t_2)$$.

Mathematically,

$$w=\arg\max_w \frac{w^TX_1^TX_1w}{w^TX_2^TX_2w}$$

I think $$X_1^TX_1$$ is the covariance matrix. Where is variance coming into picture in the above equation? How do you define variance for a vector?