The shuffle algorithm and Jordan blocks
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.
|Journal||Linear Algebra and Its Applications|
Dixon, J.D. (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