Hamilton, William Rowan (1844). “On Quaternions; or on a new System of Imaginaries in Algebra” (영어). 《Philosophical Magazine (series 3)》 25 (163): 10–13. doi:10.1080/14786444408644923. ISSN1941-5966.
Hamilton, William Rowan (1844). “On Quaternions; or on a new System of Imaginaries in Algebra (2)” (영어). 《Philosophical Magazine (series 3)》 25 (166): 241–246. doi:10.1080/14786444408644984. ISSN1941-5966.
For two elements a1 + b1i + c1j + d1k and a2 + b2i + c2j + d2k, their product, called the Hamilton product (a1 + b1i + c1j + d1k) (a2 + b2i + c2j + d2k), is determined by the products of the basis elements and the distributive law. The distributive law makes it possible to expand the product so that it is a sum of products of basis elements. This gives the following expression.....Hamilton product(Quaternion)
Using the basis 1, i, j, k of H makes it possible to write H as a set of quadruples:.....Then the basis elements are:.......and the formulas for addition and multiplication are:..........Quaternion's Ordered list form
Hamilton, William Rowan (1844). “On Quaternions; or on a new System of Imaginaries in Algebra” (영어). 《Philosophical Magazine (series 3)》 25 (163): 10–13. doi:10.1080/14786444408644923. ISSN1941-5966.
Hamilton, William Rowan (1844). “On Quaternions; or on a new System of Imaginaries in Algebra (2)” (영어). 《Philosophical Magazine (series 3)》 25 (166): 241–246. doi:10.1080/14786444408644984. ISSN1941-5966.
