...  ...  @@ 75,7 +75,7 @@ After getting the mean of the projected data, we can calculate the variance of t 


1/N \sum_{n=1}^{N} (u_{1}^Tx_{n}  u_{1}^T\overline{x})^2 = u_{1}^TSu_{1}



```






We have a definition of the variance of the data projected on $`u_1`$. We are ready to maximize it. But maximization is not an easy optimization problem. If we simply try to maximize the above equation, $`u_1`$ would go to $`\inf`$.



We now have a definition of the variance of the data projected on $`u_1`$. We are ready to maximize it. But maximization is not an easy optimization problem. If we simply try to maximize the above equation, $`u_1`$ would go to $`\infty`$.










...  ...  