Journal of Jianghan University(Natural Science Edition) ›› 2013, Vol. 41 ›› Issue (2): 7-9.

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Idempotency of Linear Combination of n Idempotent Matrices

CUI Run-qing，LI Xing-lan   

  1. School of Mathematics and Information Science，Henan Polytechnic University，Jiaozuo 454003，Henan，China
  • Online:2013-04-12 Published:2014-01-07

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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.

Key words: idempotent matrix, linear combination, idempotency

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