Richard Goldstone
Transposing Large Matrices in Small Memory
The obvious way to transpose a matrix stored in computer memory is to simply make another copy and store each row of the original matrix as a column of the copy. If the matrix is very large, the need for another copy may exceed available memory. We discuss strategies for transposing the matrix in place, using as little additional memory as possible. The mathematics involved uses some elementary facts about permutations and basic number theory.
A lot of this talk is accessible to undergraduates. Students who have had the (beginning) of an abstract algebra course will know the requisite results about permutations. They may or may not know the elementary number theory, but should be able to follow some of the discussion anyway. Faculty will have no problem with any of the talk, except possibly the part of the problem that I don't know how to do.
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