Mathematics

The Columbia Encyclopedia, 6th ed. The Concise Oxford Dictionary of English Etymology Further reading

quaternion

The Columbia Encyclopedia, 6th ed. | 2011 | Copyright

quaternion , in mathematics, a type of higher complex number first suggested by Sir William R. Hamilton in 1843. A complex number is a number of the form a + bi when a and b are real numbers and i is the so-called imaginary unit defined by the equation i² =-1. The rules for operating with complex numbers are simply those of operating with the polynomial a + bx except that i² is replaced by -1 whenever it occurs. A quaternion, an extension of this concept, is a number of the form a + bi + cj + dk when a, b, c, and d are real numbers and i, j, and k are imaginary units defined by the equations i² = j² = k² = ijk =-1. Quaternions, as well as vectors and tensors (later outgrowths of the concept of quaternions), have many important applications in mechanics.

Cite this article
Pick a style below, and copy the text for your bibliography.

MLA
Chicago
APA

"quaternion." The Columbia Encyclopedia, 6th ed.. 2011. Encyclopedia.com. 29 May. 2012 <http://www.encyclopedia.com>.

"quaternion." The Columbia Encyclopedia, 6th ed.. 2011. Encyclopedia.com. (May 29, 2012). http://www.encyclopedia.com/doc/1E1-quaterni.html

"quaternion." The Columbia Encyclopedia, 6th ed.. 2011. Retrieved May 29, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1E1-quaterni.html

Learn more about citation styles

quaternion

The Concise Oxford Dictionary of English Etymology | 1996 | | Copyright

quaternion group of four XIV; quire of four sheets XVII; (math.) XIX. — late L. quaterniō, -ōn-, f. quaternī four together (see prec.).

Cite this article
Pick a style below, and copy the text for your bibliography.

MLA
Chicago
APA

T. F. HOAD. "quaternion." The Concise Oxford Dictionary of English Etymology. 1996. Encyclopedia.com. 29 May. 2012 <http://www.encyclopedia.com>.

T. F. HOAD. "quaternion." The Concise Oxford Dictionary of English Etymology. 1996. Encyclopedia.com. (May 29, 2012). http://www.encyclopedia.com/doc/1O27-quaternion.html

T. F. HOAD. "quaternion." The Concise Oxford Dictionary of English Etymology. 1996. Retrieved May 29, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O27-quaternion.html

Learn more about citation styles

Free newspaper and magazine articles

	A note on dual quaternions and matrices of dual quaternions.(Report) Magazine article from: Scientia Magna; 1/1/2011
	Generalized galilean transformations and dual Quaternions.(Report) Magazine article from: Scientia Magna; 1/1/2009
	Fast givens transformation for quaternion valued matrices applied to... Magazine article from: Electronic Transactions on Numerical Analysis; 7/1/2005