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Symbolic matrix calculation

Is it possible to do symbolic matrix calculation with sage? What I like to do is somehow declare that U_n are unitary matrices (without giving their explicit representation). Once declared I'd like sage to exploit the unitarity when it is evaluating expressions involving U_n, like:

A=U_1.H * U_1 * U_2

should yield

A=U_2

Is this possible?

Symbolic matrix calculation

Is it possible to do symbolic matrix calculation with sage? What I like to do is somehow declare that U_n are unitary matrices (without giving their dimension or explicit representation). Once declared I'd like sage to exploit the unitarity when it is evaluating expressions involving U_n, like:

A=U_1.H * U_1 * U_2

should yield

A=U_2

Is this possible?