Annihilating polynomial
In this article, the topic of Annihilating polynomial will be addressed from different perspectives in order to analyze its impact on current society. Throughout history, Annihilating polynomial has been a topic of constant debate and its influence has transcended borders and cultures. Through this writing, we seek to delve deeper into Annihilating polynomial and understand its importance in the current context, exploring its implications and consequences. Through reflection and analysis, the aim is to offer a comprehensive vision of Annihilating polynomial and its relevance in various areas, posing questions and reflections that invite reflection and debate on this topic that is so relevant today.
A polynomial P is annihilating or called an annihilating polynomial in linear algebra and operator theory if the polynomial considered as a function of the linear operator or a matrix A evaluates to zero, i.e., is such that P(A) = 0.
Note that all characteristic polynomials and minimal polynomials of A are annihilating polynomials. In fact, every annihilating polynomial is the multiple of the minimal polynomial of an operator A.[1][2]
See also
References
- ^ Taboga, Marco. "Minimal Polynomial". statlect.com. Retrieved 17 November 2023.
- ^ Hoffman, K., Kunze, R., "Linear Algebra", 2nd ed., 1971, Prentice-Hall. (Definition on page 191 of section 6.3)