THE JACOBIAN METHOD FOR BRINGING A QUADRATIC FORM TO CANONICAL FORM

Authors

  • Jumanazarova Shodiya Otojon kizi Teacher at the Department of Physics and Mathematics Urganch State Pedagogical Institute

Keywords:

Quadratic form, Jacobian method, principal minor, coefficient, matrix, basis.

Abstract

This article extensively examines the problem of transforming a quadratic form into its canonical form. There are several methods to simplify and bring a quadratic form into a convenient and straightforward form, one of which is the Jacobian method. The article discusses how to apply the Jacobian method, its advantages, and provides examples and practical instructions related to the calculation processes. This method pays special attention to the coefficients and signs of the quadratic form.

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References

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E. R. Vrubel, Quantum Computation and Quadratic Forms in Algebra, Moscow, "Machine Teaching" Publishing, 2002.

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J. A. Tyuzukov, Algebra and Mathematical Analysis, Tashkent, "Ukituvchi" Publishing, 2015.

F. R. Gantmacher, M. G. Krein, Matrices and Methods of Working with Them, Moscow, "Nauka" Publishing, 1960.

R. S. Makarov, V. I. Kiselev, Algebra and Analytic Geometry, Moscow, "Burchak" Publishing, 2006.

M. A. Kruglov, O. A. Olkhovik, Mathematical Analysis and Quadratic Forms, Kiev, "Vishcha shkola" Publishing, 1998

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Published

2025-04-14

How to Cite

Jumanazarova Shodiya Otojon kizi. (2025). THE JACOBIAN METHOD FOR BRINGING A QUADRATIC FORM TO CANONICAL FORM. Journal of Applied Science and Social Science, 15(04), 176–178. Retrieved from https://www.internationaljournal.co.in/index.php/jasass/article/view/933

Issue

Vol. 15 No. 04 (2025): Volume 15 Issue 04

Section

Articles

License

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