how to prove definite positive

Hi, my dear friends
Plz help me with the following question
x(t) = x(t-1)+P(t-1)theta(t-1)u(t) P(t-2)theta(t-1)theta(t-1)'P(t-2)
P(t-1)=P(t-2)- ----------------------------------- 1+theta(t-1)'P(t-2)theta(t-1) Z(t) = theta(t-1)x(t-1)
if P(-1) is positive definite and theta(t) is finite for any t then prove: P(t) is positive definite at any t.
My thought is prove P(0) is p.d. ,then P(1) , then P(t)
But I was stuck
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