Hamilton’s General Quadratic Equation: Genesis and Modern Computation

Branko Sarić () and Bharath Sriraman ()
Additional contact information
Branko Sarić: University of Kragujevac, Faculty of Technical Sciences
Bharath Sriraman: University of Montana – Missoula, Department of Mathematical Sciences

A chapter in Handbook of Visual, Experimental and Computational Mathematics, 2026, pp 657-673 from Springer

Abstract: Abstract Based on Hamilton’s method of solving couple equation, defined over the field of couple numbers, as he calls them, in this chapter, the method of solving the general Hamilton quadratic equation (couple equation) is reduced to solving of the matrix quadratic equation, which is defined over the field of bireal matrices which correspond to bireal numbers. As the matrix equation is decomposed into a system of nonlinear algebraic equations (SNAE), the solutions of the matrix equation are also the solutions of the SNAE, such that the solutions of the matrix quadratic equation implicitly determine the symmetric matrices S of the null space of the SNAE. In the second part of this chapter, the matrix method for solving the SNAE, which is obtained via decomposition of Hamilton’s quadratic equation, is presented.

Keywords: Bireal numbers; Couple equation; Matrix quadratic equation (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-16368-4_84

Ordering information: This item can be ordered from
http://www.springer.com/9783032163684

DOI: 10.1007/978-3-032-16368-4_84

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().