Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지
DOI QR코드

DOI QR Code

DISTRIBUTIVE PROPERTIES OF ADDITION OVER MULTIPLICATION OF IDEMPOTENT MATRICES

  • 투고 : 2001.04.23
  • 심사 : 2011.06.01
  • 발행 : 2011.09.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Let R be a ring with identity. If a, b, $c{\in}R$ such that a+b+c = 1, then the distributive laws from addition over multiplication hold in R, that is a+(bc) = (a+b)(a+c) when ab = ba, and (ab)+c = (a+c)(b+c) when ac = ca. An application to obtains, if A,B are idempotent matrices and AB = BA = 0 then there exists an idempotent matrix C such that A + BC = (A + B)(A + C), and also A + BC = (I - C)(I - B). Some other cases and applications are also presented.

키워드

참고문헌

  1. T.W. Hungerford, Algebra, Holt, Rinehart and Winston, Inc., New York, 1974.
  2. J.R. Schott, Matrix Analysis for Statistics, second ed., John Wiley & Sons, Inc., New Jersey, 2005.
  3. J.K. Baksalary and O.M. Baksalary, Idempotency of linear combinations of two idempotent matrices. Linear Algebra Appl. 321 (2000), 3-7. https://doi.org/10.1016/S0024-3795(00)00225-1
  4. H. Ozdemir and A.Y. Ozban, On idempotency of linear combinations of idempotent matrices. Applied Mathematics and Computation. 159 (2004), 439-448. https://doi.org/10.1016/j.amc.2003.10.027
  5. C. Bu and Y. Zhou, Involutory and s+1-potency of linear combination of a tripotent matrix and an arbitrary matraix. J. Appl. Math. & Informatics 29 (2011), 485-495.