# John Williamson's papers

Below we list a few of John Williamson's papers after he became a research student in Chicago.
1. J Williamson, Conditions for associativity of division algebras connected with non-abelian groups, Trans. Amer. Math. Soc. 30 (1) (1928), 111-125.

2. J Williamson, The Complete System of Two Quaternary Quadratics, Amer. J. Math. 51 (4) (1929), 565-576.

3. J Williamson, A Special Prepared System for Two Quadratics in N Variables, Amer. J. Math. 52 (2) (1930), 399-412.

4. J Williamson, A Prepared System for Two Quinary Quadratic Forms, Amer. J. Math. 52 (4) (1930), 863-876.

5. J Williamson, Bazin's matrix and other allied matrices, Proc. Edinburgh Math. Soc. 2 (1930-31), 240-251.

6. J Williamson, A Prepared System for Two Quadratics in Six Variables, Amer. J. Math. 53 (2) (1931), 343-357.

7. J Williamson, The Product of a Circulant Matrix and a Special Diagonal Matrix, Amer. Math. Monthly 39 (5) (1932), 280-285.

8. J Williamson, On semi-commutative matrices, part I, Proc. Edinburgh Math. Soc. 3 (1932-33), 179-188.

9. J Williamson, On semi-commutative matrices, part II, Proc. Edinburgh Math. Soc. 3 (1932-33), 231-240.

10. J Williamson, The Expansion of Determinants of Composite Order, Amer. Math. Monthly 40 (2) (1933), 65-69.

11. J Williamson, The Covariants of Two Quadratic Forms in $n$ Variables, Amer. J. Math. 56 (1-4) (1934), 339-348.

12. J Williamson, On the equivalence of two singular matrix pencils, Proc. Edinburgh Math. Soc. 4 (1934-36), 224-231.

13. J Williamson, The Simultaneous Reduction of Two Matrices to Triangle Form, Amer. J. Math. 57 (2) (1935), 281-293.

14. J Williamson, The Equivalence of Non-Singular Pencils of Hermitian Matrices in an Arbitrary Field, Amer. J. Math. 57 (3) (1935), 475-490.

15. P S Dwyer,E P Starke, J Williamson and J H M Wedderburn, Problems and Solutions: Advanced Problems: Solutions: 3645, Amer. Math. Monthly 42 (1) (1935), 53-56.

16. J Williamson, The Fall Meeting of the Maryland-District of Columbia-Virginia Section, Amer. Math. Monthly 42 (4) (1935), 188-190.

17. R Robinson and J Williamson, Problems and Solutions: Advanced Problems: Solutions: 3667, Amer. Math. Monthly 42 (6) (1935), 400-401.

18. J Williamson, On the Algebraic Problem Concerning the Normal Forms of Linear Dynamical Systems, Amer. J. Math. 58 (1) (1936), 141-163.

19. J Williamson, The Idempotent and Nilpotent Elements of a Matrix, Amer. J. Math. 58 (4) (1936), 747-758.

20. J Williamson, The Spring Meeting of the Maryland-District of Columbia-Virginia Section, Amer. Math. Monthly 43 (10) (1936), 591-594.

21. J Williamson, The Conjunctive Equivalence of Pencils of Hermitian and Anti-Hermitian Matrices, Amer. J. Math. 59 (2) (1937), 399-413.

22. J Williamson, On the Normal Forms of Linear Canonical Transformations in Dynamics, Amer. J. Math. 59 (3) (1937), 599-617.

23. J Williamson, Quasi-unitary matrices, Duke Math. J. 3 (4) (1937), 715-725.

24. J Williamson, Matrices Normal with Respect to an Hermitian Matrix. Amer. J. Math. 60 (2) (1938), 355-373.

25. J W Cell and J Williamson, Problems and Solutions: Elementary Problems: Solutions: E280, Amer. Math. Monthly 45 (1) (1938), 50.

26. J Williamson, The exponential representation of canonical matrices, Amer. J. Math. 61 (1939), 897-911.

27. J Williamson, Note on a principal axis transformation for non-hermitian matrices, Bull. Amer. Math. Soc. 45 (1939), 920-922.

28. J Williamson, Simultaneous Reduction of a Square Matrix and an Hermitian Matrix to Canonical Form, Amer. J. Math. 61 (1) (1939), 81-88.

29. J Williamson, Normal Matrices Over an Arbitrary Field of Characteristic Zero, Amer. J. Math. 61 (2) (1939), 335-356.

30. J Williamson, The exponential representation of automorphs of a symmetric or hermitian matrix, Amer. J. Math. 62 (1940), 153-164.

31. J Williamson, An algebraic problem involving the involutory integrals of linear dynamical systems, Amer. J. Math. 62 (1940), 881-911.

32. J H M Wedderburn and J Williamson, Problems and Solutions: Advanced Problems: Solutions: 3856, Amer. Math. Monthly 47 (3) (1940), 182-183.

33. J Williamson, A generalization of the polar representation of nonsingular matrices, Bull. Amer. Math. Soc. 48 (1942), 856-863.

34. J A Greenwood and J Williamson, Problems and Solutions: Advanced Problems: Solutions: 4023, Amer. Math. Monthly 50 (2) (1943), 131-134.

35. C E Springer and J Williamson, Problems and Solutions: Advanced Problems: Solutions: 3994, Amer. Math. Monthly 50 (4) (1943), 271-273.

36. J Williamson, Hadamard's determinant theorem and the sum of four squares, Duke Math. J. 11 (1944), 65-81.

37. J Williamson, Note on the equivalence of nonsingular pencils of Hermitian matrices, Bull. Amer. Math. Soc. 51 (1945), 894-897.

38. F J Duarte and J Williamson, Problems and Solutions: Advanced Problems: Solutions: 4159, Amer. Math. Monthly 53 (8) (1946), 475-477.

39. J Williamson, Determinants whose elements are 0 and 1, Amer. Math. Monthly 53 (1946), 427-434.

40. D H Lehmer, D M Smiley, M F Smiley and J Williamson, Problems and Solutions: Elementary Problems: Solutions: E710, Amer. Math. Monthly 53 (9) (1946), 534-535.

41. J Williamson, Note on Hadamard's determinant theorem, Bull. Amer. Math. Soc. 53 (1947), 608-613.

Last Updated November 2007