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T:V -> V is linear.
V is finite vectorspace of dimension m^2.
T(M) = AMB where M is an mXm matrix and A, B are two fixed mXm matrices.
I want to find the trace and determinant of this transformation.
In the case where B is the indentity, I can show that the trace is m*tr(A) and the determinant is m*det(A). This is so because the matrix of this linear map can be written as an m^2Xm^2 matrix with a bunch of As on the diagonals. Do i proceed in the same way when B is not the identity? It looks complicated.
(Solving a few easy examples led me to believe that the trace and determinant is the same as in the special case...or maybe i chose bad matrices...)
Please HELP!
V is finite vectorspace of dimension m^2.
T(M) = AMB where M is an mXm matrix and A, B are two fixed mXm matrices.
I want to find the trace and determinant of this transformation.
In the case where B is the indentity, I can show that the trace is m*tr(A) and the determinant is m*det(A). This is so because the matrix of this linear map can be written as an m^2Xm^2 matrix with a bunch of As on the diagonals. Do i proceed in the same way when B is not the identity? It looks complicated.
(Solving a few easy examples led me to believe that the trace and determinant is the same as in the special case...or maybe i chose bad matrices...)
Please HELP!
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