traces on matrices with enteries in quaternions

Question

I am wondering if there exists any quaternionic valued trace $T:M_{n}(\mathbb{H}) \rightarrow \mathbb{H}$ on a quaternionic matrix? Where the trace is a linear functional on a C*-algebra with the property T(AB)=T(BA). generally, quaternions are not commutative.

score 1 · Accepted Answer · answered May 12 '19 at 16:51

1

You could try $\frac12\sum_{ij}(A_{ij}B_{ji}+B_{ji}A_{ij})$ to restore commutativity.

answered May 12 '19 at 16:51

J.G.

115,835

1

Thank you so much that is interesting. – Emilly May 12 '19 at 20:59

traces on matrices with enteries in quaternions

1 Answers1