P is a symmetric positive definite matrix. I want to know under what condition of matrix A will the matrix A'P+PA be positive definite, assuming A,P are square matrices of same order.
A'P+PA is a symmetric matrix proof: let w=A'P then W'=(A'P)'=PA W=(W+W')/2 + (W-W')/2 where (W+W')/2 is symmetric and (W-W')/2 is skew symmetric therefore A'P+PA is symmetric (equals symmetric part w+w')
Basically I want to clarify if both A and P must be symmetric positive definite matrix for A'P+PA to be positive definite (or positive semi def). I am interested in knowing the properties of A which would ensure positive definiteness (or positive semi def) of A'P+PA.