I have a long expression involving matrices that I derived using the NCAlgebra package. Can I simplify the trace of the expression?
For example, say b
is a scalar (commutes with all) and x
and y
are matrices (non-commutative). Can I simplify Tr[b x.y.y + b y.x.y]
to 2b Tr[x.y.y]
using the properties of the trace?
Thanks, that is what I am going for (although I don't quite understand the code) but I only have version 8.
The expression is given below, where e
and r
are scalars, q
and v
are matrices and the double star (**
) denotes products of non-commutative elements. I've done it by hand, but I want to be able to simplify the trace of this with Mathematica (and others which are much longer).
e^2 q ** q - e r q ** v - e r v ** q + r^2 v ** v -
1/12 e^3 r q ** q ** q ** v + 1/12 e^3 r q ** q ** v ** q +
1/24 e^2 r^2 q ** q ** v ** v + 1/12 e^3 r q ** v ** q ** q -
1/12 e^2 r^2 q ** v ** q ** v - 1/12 e^2 r^2 q ** v ** v ** q +
1/24 e r^3 q ** v ** v ** v - 1/12 e^3 r v ** q ** q ** q +
1/6 e^2 r^2 v ** q ** q ** v - 1/12 e^2 r^2 v ** q ** v ** q -
1/24 e r^3 v ** q ** v ** v + 1/24 e^2 r^2 v ** v ** q ** q -
1/24 e r^3 v ** v ** q ** v + 1/24 e r^3 v ** v ** v ** q