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CMS Adam Rogers from IWMS-16 Windsor 1-3 June 2007 Slides 42-46 (43-44 coloured by Ian Cameron)

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N.B. The compound magic square contribution of Adam Rogers was not included in the conference publication in Linear Algebra and Its Applications 2009 as it was intended for a fuller follow-up.

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Science in the Universe of the Matrix Elements 1..n 2 Science in the Universe of the Matrix Elements 1..n 2 Windsor 2007 June 1-3 (In preparation) Peter Loly & Ian Cameron With Adam Rogers, Daniel Schindel and Walter Trump With Walter Trump, Adam Rogers & Daniel Schinde Critical funding from the Winnipeg Foundation in 2003.

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4 Compound Squares Wayne Chan & Peter Loly, Mathematics Today 2002 Harm Derksen, Christian Eggermont, Arno van den Essen, Am. Math. Monthly (in press) Matt Rempel, Wayne Chan, and Peter Loly Adam Rogers’ Kronecker product

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5 Compounded Lo-shu (1275 Yang Hui; Cammann) 313629768174131811 303234757779121416 352833807378171015 222720404538586356 212325394143575961 261924443742625560 677265 492 495447 666870 357 485052 716469 816 534651

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6 Second Compound Method (1275 Yang Hui; Cammann) 317613368118297411 224058274563203856 67 4 4972 9 5465 2 47 307512327714347916 213957234159254361 66 3 4868 5 5070 7 52 358017287310337815 264462193755244260 71 8 5364 1 4669 6 51

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7 Kronecker Product For 2 nd order A, any B

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8 2004 Adam Rogers (4 th year Quantum Mechanics) E N is Nth order square of 1’s A M and B N are Mth and Nth order squares Associative Compounding: R A = E M B N + N k (A M E N ) Distributive Compounding: R D = B N E M + N k (E N A M ) Given the EVs and SVDs of A and B, Rogers can find those for both compound methods (k=2 for squares, 3 for cubes, etc.,)

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