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

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)

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