I would like to ask you something regarding the trace of a matrix (the value of the diagonal after adding all its members, a value which is said to remain constant independently from base changes):
Do matrices with trace value zero constitute a (sub)group? If so, which properties tell them apart from matrices with non-zero trace values? Should a matrix with diagonal entries such as , say, [2, -3, 1], group together with that showing [0,0,0]?
I am particularly interested in those cases in which all the members of the diagonal equal zero. Do they have interesting algebraic properties as compared with the other zero trace matrices and the nonzero matrices altogether?
Thanks in advance.