In the paper we formulate the sufficient condition which must satisfy an irreducible acyclic matrix A to be alpha-scalar diagonally stable. Moreover we consider the existence of positive definite diagonal matrix C and positive definite alpha-scalar matrix D such that DA+ATD=C. These conditions are the generalizations of several theorems which are the necessary and sufficient condition which must satisfy square matrix A to exist positive diagonal matrices C and D such that DA+ATD=C.
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