Suppose A=LLT, where L is a lower triangular matrix whose diagonal entries are all positive. If another lower triangular matrix P also satisfies A=PPT, and the diagonal entries of P are also positive, show that P=L.
This are my steps.
LLT = PPT
P-1L=(L-1P)T=D where D is a diagonal matrix.
But I am stuck after this. I have not used the property that the diagonal entries of L and P are positive. Does this imply that D=I?
Your help is greatly appreciated.