Such a definition (but not *the* definition, I suppose) can be found in [*Clifford Algebras and the Classical Groups*][1] by Ian Porteous (see Chapt. 13). 

It is based on the classification of real algebra anti-involutions of $A(n)$ where $A$ is equal to $K$ or $^2K$, and $K = \mathbb R$, $\mathbb C$ or $\mathbb H$.  By the theorem below there are ten cases. In each case there is a corresponding family of groups of correlated automorphisms analogous to the orthogonal groups.   

> **Theorem.** Let $\xi$ be an irreducible correlation on a right $A$-linear space of finite dimension $> 1$, and therefore equivalent to a symmetric or skew correlation. Then $\xi$ is equivalent to one of the following ten types, these 
being mutually exclusive. 

>1. A symmetric $\mathbb R$-correlation; 
2. A symmetric, or equivalently a skew, $^2\mathbb R^\sigma$-correlation; 
3. A skew $\mathbb R$-correlation; 
4. A skew $\mathbb C$-correlation; 
5. A skew $\tilde{\mathbb H}$- or equivalently a symmetric $\overline{\mathbb H}$-correlation; 
6. A skew, or equivalently a symmetric,$^2\overline{\mathbb H}^\sigma$ -correlation; 
7. A symmetric $\tilde{\mathbb H}$-, or equivalently a skew, $\overline{\mathbb H}$-correlation; 
8. A symmetric $\mathbb C$-correlation; 
9. A symmetric, or equivalently a skew, $\overline{\mathbb C}$-correlation; 
10. A symmetric, or equivalently a skew, $^2\overline{\mathbb C}^\sigma$-correlation.

> The ten families of classical groups are as follows, where $p+q=n$:

>1. $O(p, q; \mathbb R)$ or $O(p, q)$, with $O(n) = 0(0, n)$; 
2. $GL(n;\mathbb R)$; 
3. $Sp(2n;\mathbb R)$;  
4. $Sp(2n;\mathbb C)$; 
5. $Sp(p,q;\mathbb H)$ or $Sp(p,q)$, with $Sp(n)= Sp(0,n)$; 
6. $GL(n;\mathbb H)$;
7. $O(n;\mathbb H)$; 
8. $O(n;\mathbb C)$; 
9. $U(p,q)$, with $U(n)=U(0,n)$; 
10. $GL(n;\mathbb C)$. 



 


[1]: http://books.google.com.ua/books?id=KZ-O_BhLSfkC&printsec=frontcover&dq=porteous+clifford+algebras+and+the+classical+groups&source=bl&ots=Q-RPvXYy9x&sig=LR5t69NyoQx_ufIOAidj8R1_7dQ&hl=en&ei=ioIaTae-CYi28QPTs82ZBQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBoQ6AEwAA#v=onepage&q&f=false