Search results for "Adjugate matrix"

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On complete set of solutions for polynomial matrix equations

1990

Abstract In this paper we introduce the concept of co-solution of a polynomial matrix equation which permits us to obtain necessary and sufficient conditions so that a set of solutions be a complete set.

Discrete mathematicsAdjugate matrixMinimal polynomial (linear algebra)Stable polynomialApplied MathematicsCompanion matrixApplied mathematicsMonic polynomialPolynomial matrixCharacteristic polynomialMatrix polynomialMathematicsApplied Mathematics Letters
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Inversion of matrix pencils for generalized systems

1993

Abstract This paper clarifies the nature of the Leverrier-Faddeev algorithm for generalized and state-space systems. It presents useful diagrams for recursive computation of the coefficients of the characteristic polynomial and the coefficient matrices of the adjoint matrix for various matrix pencils. A simplified case covers recursive equations and diagrams for inversion of the second-order matrix pencil (Es2 + A1s + A0) where E may be singular. The appendix provides two examples of mechanical and heat exchange systems which can be described by the generalized models.

State-transition matrixComputer Networks and CommunicationsApplied MathematicsMathematicsofComputing_NUMERICALANALYSISSingle-entry matrixInversion (discrete mathematics)Matrix (mathematics)Adjugate matrixControl and Systems EngineeringComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONSignal ProcessingCalculusMatrix pencilState spaceApplied mathematicsMathematicsCharacteristic polynomialJournal of the Franklin Institute
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