None of the above answers are satisfactory. My guess is that many beginners in R would have the same question and they deserve a clear and complete answer.

In maths, the trace of a matrix is defined only for squared matrix and the canonical way to compute the trace of a matrix in R is

sum(diag(x))

In particular:

• it is against all recommendations to use such unexported functions as stats:::Tr().
• the function matrix.trace() of the package matrixcalc has no added value.
• the function tr() of the package psych is, as described by the authors, doing exactly sum(diag()).
• writing a function to test that an object is squared or numeric is useless since the error messages thrown by sum(diag()) are clear in this matter.
• using eigenvalues is incredibly complex for such a simple operation.

It is therefore strongly recommended to stick with sum(diag()) which is simple and efficient even for very large matrices. sum() is a primitive function and the complete code of diag() is available here.