"weigh" different variance covarance matrixes so my question if I have a set of weights which sums to 1 (say: [0.2,0.2,0.6]) which would represent my states of the world and I have forecasted 3 different variance covariance matrixes (all of which are internally coherent), would I get a coherent (=positive definitive ) and usable variance covariance matrix at the end?
that is will 
w1 * sigma1 + w2 * sigma2 + w3 * sigma3 =  FinalSigma
with FinalSigma internally coherent (=positive definite)?
 A: Presuming the weights are all nonnegative, which I presume you intended, but did not explicitly state, then a weighted sum of covariance matrices will be a covariance matrix, meaning that it is symmetric positive semi-definite.  If the covariance matrices are all positive definite, then their weighted sum will be positive definite.
To simplify the discussion, I will assume all weights are in fact positive, since otherwise the corresponding covariance matrix (having zero weight) can be removed from consideration. 
Clearly, symmetry is preserved by taking the (non-negative) weighted sum of symmetric matrices.  As for positive definiteness or positive semi-definitness, note that the matrix C will be positive definite (or semi-definite), according as $x^t C x$ > 0 (respectively >= 0) for all x not equal to zero.  Clearly, multiplying C by a non-negative number preserves these inequalities.  Forming the weighted sum and summing these > 0 or >= 0 terms shows that positive definiteness or positive semi-definiteness is preserved.
