As the title says I need to make sure I understand exactly what a normalized trace is. Everywhere I've looked, including here I find references to the trace of a normalized matrix, but I am not comfortable simply assuming a normalized trace = trace of normalized matrix.

Edit: I should have specified that the matrix in question is a square 3x3 matrix

Thanks in advance.

  • 1
    $\begingroup$ In what context? $\endgroup$ Sep 7, 2015 at 16:53
  • $\begingroup$ @Mariano For my case it's coming from this paper: section 3.2.3. Relating to a matrix representing a deformation of a volume by a gradient of a field. $\endgroup$
    – Tuffwer
    Sep 7, 2015 at 16:56

1 Answer 1


Apparently I just didn't spend quite enough time looking.

According to this book Clifford Algebras: An Introduction (by D. J. H. Garling) the normalized trace of a square matrix is just the trace of the matrix divided by the dimension of the matrix.

For a 3x3 matrix A the normalized trace would be the tr(A)/3.


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