# how to find percentage of total variation from population covariance matrix and population mean matrix

I have a matrix with dimension nxp. No:of observations are not known. But no: of variables is 3. So p=3. Population mean is defined as µ1=1,µ2=-1,µ3=2.

$$\sum$$=

$$\begin{bmatrix} 1 & k & 0\\ k & 1 & k\\ 0 & k & 1\end{bmatrix}$$ How to find the value of k such that the principal components PC1 and PC2 account for more than some percentage (say 75%) of total variation of X?

• It looks like Sigma is a correlation matrix not a covariance matrix because of the ones on the diagonal. Could you precise what is X ? – manu190466 Apr 10 '20 at 7:19
• X = (X1, X2, X3) distributed as N3(µ, Σ). I did determinant( Σ - lamda * I ) = 0. To get value of k in terms of lamda. – StatsMonkey Apr 10 '20 at 11:52
• When you say "they account ..." what would you mean exactly ? The two first eigenvectors ? Please edit your question to give more details. – manu190466 Apr 10 '20 at 12:28
• Yes..There was mistake in question. I edited – StatsMonkey Apr 10 '20 at 13:11