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Aug 5, 2015 at 15:10 comment added bbgodfrey @J. M. If the matrices are related by similarity transformations, then those relationships need to be provided in the question. Or, perhaps I misunderstand your comment. In any case, a specific set of equations, perhaps involving SO(3), might be helpful.
Aug 5, 2015 at 14:47 comment added J. M.'s missing motivation If m and n are similar (which is what the OP says), certainly there ought to be some t that will do the job.
Aug 5, 2015 at 14:42 history answered bbgodfrey CC BY-SA 3.0