THE DOUBLE OPERATION OF NILPOTENT AND DUAL OPERATIONS

THE DOUBLE OPERATION OF NILPOTENT AND DUAL OPERATIONS

Authors

  • Umarov Habibullo Rahmatullaevich Senior teachers of Gulistan State University
  • Goyibnazarov Habibullo Rahmatullaevich Senior teachers of Gulistan State University

Keywords:

operator, composition of operators, nilpotent operator, height (index) of nilpotent operator, special operator, special operatorright set of operators

Abstract

In this article, it is proved that any non-nilpotent eigenoperator can be represented by a unique method in the form of a proper sum of nilpotent and eigenoperators. It was also shown that nilpotent operators have all eigenvalues ​​equal to zero, and vice versa, if an operator has all eigenvalues ​​equal to zero, then this operator is a nilpotent operator.

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Published

2024-11-25

How to Cite

Rahmatullaevich, U. H. ., & Rahmatullaevich, G. H. . (2024). THE DOUBLE OPERATION OF NILPOTENT AND DUAL OPERATIONS. JOURNAL OF THEORY, MATHEMATICS AND PHYSICS, 3(11), 52–58. Retrieved from http://jtmp.innovascience.uz/index.php/journal/article/view/216

Issue

Vol. 3 No. 11 (2024): JOURNAL OF THEORY, MATHEMATICS AND PHYSICS

Section

Articles