The Jordan Form Problem for C = AB : the Balanced , Diagonalizable Case
نویسندگان
چکیده
We consider a key case in the fundamental and substantial problem of the possible Jordan canonical forms of A, B,C ∈Mn(F ) when C = AB. If A ∈ M2k(F ) (respectively B, C ∈ M2k(F ) ) is diagonalizable with two distinct eigenvalues a1, a2 (respectively b1, b2, and c1, c2), each with multiplicity k, and when C = AB, all possibilities for a1, a2, b1, b2, c1, c2 are characterized. The possibilities are much more restrictive than the obvious determinant condition: (a1a2b1b2) = (c1c2) allows. This is then used to settle the general, two eigenvalue per matrix, diagonalizable case of the Jordan form problem for C = AB. AMS Classification: 15A23.
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