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
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
Add image file
Upload is a website by engineers for engineers. It is not affiliated with any of manufacturers or vendors discussed here. All logos and trade names are the property of their respective owners.