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CMS Adam Rogers from IWMS-16 Windsor 1-3 June 2007

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

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CMS Adam Rogers from IWMS-16 Windsor 1-3 June 2007

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

  2. 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.

  3. Science in the Universe of theMatrix Elements 1..n2Windsor 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.

  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

  5. Compounded Lo-shu(1275 Yang Hui; Cammann)

  6. Second Compound Method(1275 Yang Hui; Cammann)

  7. Kronecker Product • For 2nd order A, any B

  8. 2004 Adam Rogers(4th year Quantum Mechanics) • EN is Nth order square of 1’s • AM and BN are Mth and Nth order squares • Associative Compounding: • RA = EMBN + Nk (AM EN) • Distributive Compounding: • RD = BNEM + Nk (EN AM) • 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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