solution

M1,M2, ..., MnMn(R)
det(Pn
1MtM)≥0
S+(R)
MS+(R)
det(M)≥.
A B S+(R)
det(A+B)≥det(A) + det(B
A
D A =tP P
B=tP DP
det(A+B) = (det(P))2det(D+I) = (det(P)2Qn
1(1 + ap)≥
(det(P))2(1 + (Qn
1ap)) = det(A) + det(B)
apD
B
A1, A2, ..., ApS+(R)det PP
u=1 Ai≥
Pp
i=1 (detAi)

MpMp
det p
X
i=1
MiMi!≥
p
X
i=1
detMt
iMi
det(Mt
iMi) (detMi)2≥0.