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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?

Thanks in advance

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