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)

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