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 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.

4. 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. 5 Compounded Lo-shu (1275 Yang Hui; Cammann) 313629768174131811 303234757779121416 352833807378171015 222720404538586356 212325394143575961 261924443742625560 677265 492 495447 666870 357 485052 716469 816 534651

6. 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

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

8. 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.,)