Journal of Soviet Mathematics

, Volume 28, Issue 3, pp 341–353 | Cite as

Connection between the spectral problem for linear matrix pencils and some problems of algebra

  • V. N. Kublanovskaya


We suggest a method by which the solution of systems of nonlinear algebraic equations in one and two variables can be reduced to the spectral problem for linear pencils of two matrices and for a system of two matrix pencils of two matrices, respectively. This method is substantially different from the traditional methods of solution; at the same time it is useful for the study of the solvability and the determination of the number of solutions of such systems. We propose a modification of the well-known elimination method for the solution of nonlinear algebraic systems of two equations in two unknowns which provides a new approach to studying and solving the problem.


Traditional Method Algebraic Equation Linear Matrix Spectral Problem Algebraic System 
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Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • V. N. Kublanovskaya

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