LI Xing-lan
Abstract
Let P1,P2…Pn be n different nonzero mutually commutative m×m idempotent matrices and c1,c2…cn be nonzero complex number,a set of sufficient conditions are given for the matrix P=c1P1+c2P2+…+cnPn still to be an idempotent matrix under the condition that the mutual product is zero or the mutual product is equal to either one.
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Let P1,P2…Pn be n different nonzero mutually commutative m×m idempotent matrices and c1,c2…cn be nonzero complex number,a set of sufficient conditions are given for the matrix P=c1P1+c2P2+…+cnPn still to be an idempotent matrix under the condition that the mutual product is zero or the mutual product is equal to either one.
Key concepts: Idempotence, Idempotent matrix, Mathematics, Product (mathematics), Combinatorics, Matrix (chemical analysis), Commutative property, Zero (linguistics)