Matrix calculus for statistics
2
I want to calculate the variance of a sum of random variables $ (X_1+X_2) $ . Doing statistics, I have to learn maths starting from the end and it is quite difficult, yet very interesting (please consider that I only have the very basic skills in maths). For now I am doing this calculus manually with the formula $ mathrm{var}(X_1+X_2) = mathrm{var}(X_1) + mathrm{var}(X_2) + 2mathrm{cov}(X_1,X_2)$ . But I am now facing much larger sums (with some minus) and being able to do so with matrix calculation would save me a lot of time (and would be very satisfying too). I searched every resource in matrix calculus but couldn't find anything usable with my knowledge. How can I do this calculus from the variance-covariance matrix $$ begin{pmatrix} mathrm{var}(X_1) & mathrm{cov}(X_1,X_2) \ mathrm{cov}(X_1,