# matrix algebra

1. ### Correct Cross Validation. How to calculate the projected R Squared or Residual Sum Sq

Hi, I have read into the subject of finding good estimators to determine the goodness of fit when the regression on a trainingset is projected on a testset (unseen data). I have found a lot of scientific papers but I get completely lost in terminologie and very complex equations I do not...
2. ### Showing Left Side to Right Side.

Let \mathbf x is a (p\times 1) vector, \mathbf\mu_1 is a (p\times 1) vector, \mathbf\mu_2 is a (p\times 1) vector, and \Sigma is a (p\times p) matrix. Now I have to show -\frac{1}{2}(\mathbf x-\mathbf\mu_1)'\Sigma^{-1}(\mathbf x-\mathbf\mu_1)+\frac{1}{2}(\mathbf...
3. ### Why does the determinant always equal zero for a matrix of consecutive numbers?

Hi. Why does the determinant always equal zero for a matrix of consecutive numbers? This applies whether the consecutive numbers are in the matrix starting from smallest to largest, or vice versa. It also applies irrespective of whether they are entered row then column or vice versa, which...