Tr

Tr computes the trace of a rectangular matrix. Some examples are given in

the next two cells.

Computing the trace of a matrix is a common operation in linear algebra. Mathematica generalizes the notion of trace to make it so we can compute Tr[vector]. When Tr is given a vector we get the sum of the elements. The use of (Tr) in the next cell does the same thing as . Rob Knapp showed us that when a vector is a packed array is much faster than . My timing tests vary, but I found Tr to be at least 25 times faster when given a packed array.

Next I give some examples that go down to different levels of a tensor.

By default Tr works at the deepest level, which is level 4 in this example.

Next Tr is used at level 3.

Next Tr is used at level 2.

Finally Tr is used at level 1.

Created by Mathematica (May 16, 2004)