What is the origin of unit vector notation? (i,j,k) - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-18T11:33:09Z http://mathoverflow.net/feeds/question/78950 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/78950/what-is-the-origin-of-unit-vector-notation-i-j-k What is the origin of unit vector notation? (i,j,k) Owen Coutts 2011-10-24T04:14:24Z 2011-10-24T04:52:21Z <p>What is the origin of this notation? Who coined them and for what purpose?</p> http://mathoverflow.net/questions/78950/what-is-the-origin-of-unit-vector-notation-i-j-k/78952#78952 Answer by Hanxiong Zhang for What is the origin of unit vector notation? (i,j,k) Hanxiong Zhang 2011-10-24T04:52:21Z 2011-10-24T04:52:21Z <p>Maybe it originates from Hamilton's quaternions $\mathbb{H}$, which has a basis $1,i,j,k$ as a real vector space, and the multiplications there, namely, $i\cdot j=k, j\cdot k=i, k\cdot i=j$ correspond exactly to the wedge product in $\mathbb{R}^3$. So $\mathbb{R}^3$ can be viewed as the imanginary part of $\mathbb{H}$.</p> <p>Anyway, this is just my understanding or my guess. </p>