Help me : Transformation of multivariate distribution

K=(k1,
k2,
k3)

P=(p11,p12,p13,
p21,p22,p23,
. . .
. . .
. . .
pn1,pn2,pn3)

Q = P*K

Random vector K have a distribution f(K). P is a constant matrix.
What is the distribution of Q?

I tried Jacobian. I pad zeros to make K n-dim vector, and pad random submatrix to make P a nxn matrix. But I cannot get a unique distribution of Q, because of the random submatrix padded to P.

Many thanks
.

Relevant Pages