Total reduction of linear systems of operator equations with the system matrix in the companion form | Zendy

Ivana Jovović | Zendy

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Total reduction of linear systems of operator equations with the system matrix in the companion form

Author(s) -

Ivana Jovović

Publication year - 2013

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim1307117j

Subject(s) - matrix (chemical analysis) , reduction (mathematics) , mathematics , operator (biology) , linear system , basis (linear algebra) , system of linear equations , state transition matrix , square matrix , mathematical analysis , symmetric matrix , physics , geometry , eigenvalues and eigenvectors , materials science , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , composite material , gene

We consider a total reduction of a nonhomogeneous linear system of operator equations with the system matrix in the companion form. Totally reduced system obtained in this manner is completely decoupled, i.e., it is a system with separated variables. We introduce a method for the total reduction, not by a change of basis, but by finding the adjugate matrix of the characteristic matrix of the system matrix. We also indicate how this technique may be used to connect differential transcendence of the solution with the coefficients of the system.

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