The real numbers have a conjugation operation $\overline{a} = a$, and we can define the conjugate-transpose operation $A \mapsto A^\dagger$ on matrices. (Here this is just the transpose, because the conjugate is trivial). We say that a matrix satisfying $A^\dagger = A$ is symmetric, and a matrix satisfying $A^\dagger A = I$ is orthogonal.
The complex numbers have a conjugation operation $\overline{a + bi} = a - bi$, and we can define the conjugate-transpose operation $A \mapsto A^\dagger$ on complex matrices. We say that a matrix satisfying $A^\dagger = A$ is hermitian, and a matrix satisfying $A^\dagger A = I$ is unitary.
The quaternions have a conjugation $\overline{a + bi + cj + dk} = a - bi - cj - dk$, and we can define the conjugate-transpose operation $A \mapsto A^\dagger$ on quaternion matrices. Is there a special name for the "self-adjoint matrices" (those satisfying $A^\dagger = A$) or the "metric preserving" matrices (those satisfying $A^\dagger A = I$)?
I note for those interested that it is possible to formalise all of this in a basis-free way, by defining the notion of an inner product on a vector space over the quaternions. Many of the same theorems still hold, for instance the self-adjoint operators admit an orthonormal eigenbasis with all real eigenvalues.