A shuffle is the horizontal interchange of a pair of blocks of the same size in a matrix. A general algorithm using row reduction and shuffles was first introduced by Luenberger, and then used by Anstreicher and Rothblum to give an algorithm to compute generalized nullspaces. We present a new, concise proof of this shuffle algorithm, and show how the shuffle algorithm can be used in deriving the Jordan blocks for a square matrix with known eigenvalues.

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Persistent URL dx.doi.org/10.1016/0024-3795(90)90264-D
Journal Linear Algebra and Its Applications
Dixon, J.D, Poland, J.C. (J. C.), Pressman, I, & Ribes, L. (1990). The shuffle algorithm and Jordan blocks. Linear Algebra and Its Applications, 142(C), 159–165. doi:10.1016/0024-3795(90)90264-D