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Jordan Form

Mariner 667 Maple
February 08 2007
0
There was a discussion on comp.soft-sys.maths.maple about how well Maple obtains the Jordan Normal Form of a (square) matrix. LinearAlgebra[JordanForm] is limited to matrices of integers, so it can make severe demands on computer memory; furthermore, in practice, one is often confronted with floating point data. However, linalg[jordan] operates on matrices of both integer and floating point data. Some doubts were expressed about the accuracy of linalg[jordan]; the need to increase the setting of Digits to maintain accuracy was highlighted. Subsequently, I produced this worksheet to demonstrate that linalg[jordan] is reasonably accurate with matrices up to 35 x 35 entries of random floating point data lying between –99 and 99. I am indebted to Dave Linder for help in devising a procedure to sort the vectors of complex eigenvalues. Joe Riel drew attention to the instability of the Jordan Form algorithm and recommended use of the Schur Form. J. Tarr View 724_linalg Jordan Form.mw on MapleNet or Download 724_linalg Jordan Form.mw
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