# What is the origin of unit vector notation? (i,j,k)

What is the origin of this notation? Who coined them and for what purpose?

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I'm retagging your question, since it is really about history (and not about algebraic geometry) – Yemon Choi Oct 24 '11 at 4:16
Just a guess: Brougham Bridge, Dublin, Oct. 16 1843, W.R. Hamilton, quaternions. en.wikipedia.org/wiki/History_of_quaternions – Theo Buehler Oct 24 '11 at 4:43
While this is a mildly interesting historical question, I do not think MO should become a repository for asking 'where does this common notation come from?' style questions. Searching on google for "history of mathematical notation" gives a number of interesting pages. – David Roberts Oct 24 '11 at 6:41
...but admittedly not the answer to this question. – David Roberts Oct 24 '11 at 6:42

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 $\mathbb{H}$.
One could then speculate that there were the complex numbers with $i$ an imaginary number, and when Hamilton needed three more of them, he just used the next letters in the alphabet. – Julien Puydt Oct 24 '11 at 11:13