An introduction to the rational canonical form

• Main Authors: Gador, Cristina Lorelei Q., Villarico, Beverly C.
• Format: text
• Language: English
• Published: Animo Repository 1993
• Subjects: Matrices; Algebras, Linear; Rational equivalence (Algebraic geometry); Linear operators; Mathematics > Formulae
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16110
• Institution: De La Salle University

This thesis presents the rational canonical form for linear operators and matrices. In the analysis of linear operators on a finite-dimensional vector space, eigenvalues and eigenvectors are useful tools provided that the characteristic polynomial of the linear operator factors into a product of polynomials of degree one. On the other hand, rational canonical form can be used for the analysis of any linear operator on a finite-dimensional vector space including those whose characteristic polynomial cannot be factored out into linear polynomials. The rational canonical form can be obtained by using the structure theorems which are derived based on monic irreducible factors of the characteristic polynomial of linear operators and matrices.The researchers provide a review of definitions and concepts and theorems that are necessary for the discussion of the rational canonical form.