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Yorick Hardy (e-mail) (website/alternate)

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Books

• Bose, Spin and Fermi Systems: Problems and Solutions
• Classical and Quantum Computing with C++ and Java Simulations
• Computer Algebra with SymbolicC++
• Matrix Calculus and Kronecker Product: A Practical Approach to Linear and Multilinear Algebra
• Problems and Solutions for Groups, Lie Groups, Lie Algebras with Applications
• Problems and Solutions in Introductory and Advanced Matrix Calculus
• Problems and Solutions in Quantum Computing and Quantum Information
• Problems and Solutions in Scientific Computing
• Quantum Mechanics using Computer Algebra

Links

• Alexandre Hardy
• International School for Scientific Computing
• Lambda the Ultimate
• NetBSD operating system
• SymbolicC++ computer algebra system (also on SourceForge)
• Willi-Hans Steeb

Publications

arXiv also has a list of preprints.

1. A. Fošner, Y. Hardy and B. Zinsou,
   Block determinants, partial determinants and the exponential map,
   Linear and Multilinear Algebra, in press, 2024.
   
2. Y. Hardy and B. Zinsou,
   Canonical forms for boundary conditions of self-adjoint differential operators,
   Journal of Applied Analysis & Computation, 14, 1854—1868, 2024.
   
3. Y. Hardy, W.-H. Steeb and G. Kemp,
   Matrices and Their (Un)Faithful Fermi-quadratic Forms,
   International Journal of Theoretical Physics, 58, 1470—1481, 2019.
4. Y. Hardy and A. Fošner,
   Linear maps preserving Kronecker quotients,
   Linear Algebra and its Applications, 556, 200—209, 2018.
   
5. W.-H. Steeb and Y. Hardy,
   Eigenvalue Problem, Spin Systems, Lie Groups, and Parameter Dependence,
   Zeitschrift für Naturforschung A, 70, 605—609, 2015.
6. W.-H. Steeb and Y. Hardy,
   Exponential of a matrix, a nonlinear problem, and quantum gates,
   Journal of Mathematical Physics, 56, 012201, 2015.
   Preprint available on arXiv.org.
7. Y. Hardy,
   On Kronecker Quotients,
   Electronic Journal of Linear Algebra, 27, 172—189, 2014.
   Also available on arXiv.org.
8. W.-H. Steeb and Y. Hardy,
   Exceptional points, non-normal matrices, hierarchy of spin matrices and an eigenvalue problem,
   International Journal of Modern Physics C, 25, 1450059, 2014.
   Preprint available on arXiv.org.
9. W.-H. Steeb and Y. Hardy,
   Majorana Fermions on a Lattice and a Matrix Problem,
   Zeitschrift für Naturforschung, 69a, 108—110, 2014.
   Preprint available on arXiv.org.
10. W.-H. Steeb and Y. Hardy,
    An eigenvalue problem for a Fermi system and Lie algebras,
    Quantum Information Processing, 13, 299—308, 2014.
    Preprint available on arXiv.org.
11. Y. Hardy, A. Fošner and W.-H. Steeb,
    Cayley transform and the Kronecker product of Hermitian matrices,
    Linear Algebra and its Applications, 439, 4023—4031, 2013.
    Preprint available on arXiv.org.
12. W.-H. Steeb and Y. Hardy,
    Hamilton Operators, Discrete Symmetries, Brute Force and SymbolicC++,
    International Journal of Modern Physics C, 24, 1250095, 2013.
    Preprint available on arXiv.org.
13. Y. Hardy and W.-H. Steeb,
    A Sequence of Quantum Gates,
    International Journal of Geometric Methods in Modern Physics, 9, 1220013, 2012.
    Preprint available on arXiv.org.
14. W.-H. Steeb and Y. Hardy,
    Dynamical Systems, Vector Fields and Commutators,
    Nonlinear Dynamics of Electronic Systems, Proceedings of NDES 2012, 1—4, 2012.
15. W.-H. Steeb, Y. Hardy and I. Tanski,
    Vector Fields, Variational Equations and Commutators,
    International Journal of Bifurcation and Chaos, 22, 1250190, 2012.
16. W.-H. Steeb, Y. Hardy and J. de Greef,
    Spin Hamilton Operators, Symmetry Breaking, Energy Level Crossing, and Entanglement,
    Zeitschrift für Naturforschung, 67a, 608—612, 2012.
    Preprint available on arXiv.org.
17. W.-H. Steeb and Y. Hardy,
    Entanglement, Kronecker Product, Pauli Spin Matrices and a Nonlinear Eigenvalue Problem,
    Open Systems & Information Dynamics, 19, 1250004, 2012.
18. Y. Hardy and W.-H. Steeb,
    Unitary Matrices and Commutators,
    International Journal of Geometric Methods in Modern Physics, 8, 1583—1592, 2011.
19. W.-H. Steeb, Y. Hardy and I. Tanski,
    Vector Product and an Integrable Dynamical System,
    Communications in Theoretical Physics, 56, 992—994, 2011.
20. W.-H. Steeb and Y. Hardy,
    N-tangle, Entangled Orthonormal Basis, and a Hierarchy of Spin Hamilton Operators,
    Zeitschrift für Naturforschung, 66a, 615—619, 2011.
21. Y. Hardy and W.-H. Steeb,
    Genetic Algorithms and Optimization Problems in Quantum Computing,
    International Journal of Modern Physics C, 21, 1359—1375, 2010.
22. Y. Hardy and W.-H. Steeb,
    Vec-Operator, Kronecker Product and Entanglement,
    International Journal of Algebra and Computation, 20, 71—76, 2010.
23. W.-H. Steeb and Y. Hardy,
    A Chaotic Map and Data Communication,
    Zeitschrift für Naturforschung, 65a, 613—614, 2010.
24. W.-H. Steeb and Y. Hardy,
    Unitary Operators, Entanglement, and Gram-Schmidt Orthogonalization,
    International Journal of Modern Physics C, 20, 891—899, 2009.
25. W.-H. Steeb and Y. Hardy,
    A hierarchy of Hamilton operators and entanglement,
    Central European Journal of Physics, 7, 854—859, 2009.
26. W.-H. Steeb and Y. Hardy,
    Quantum optics networks, unitary operators and computer algebra,
    International Journal of Modern Physics C, 19, 1069—1078, 2008.
27. Y. Hardy and D. Sabatta,
    Encoding, symbolic dynamics, cryptography and C++ implementations,
    Physics Letters A, 366, 575—584, 2007.
28. W.-H. Steeb and Y. Hardy,
    One-Dimensional Cellular Automata, Conservation Laws and Partial Differential Equations,
    Zeitschrift für Naturforschung, 62a, 569—572, 2007.
29. Y. Hardy and W.-H. Steeb,
    Decomposing the SWAP Quantum Gate,
    Journal of Physics A: Math. and Gen, 39, 1463—1467, 2006.
30. W.-H. Steeb and Y. Hardy,
    Quantum Gates and Hamilton Operators,
    International Journal of Theoretical Physics, 45, 953—961, 2006.
31. W.-H. Steeb and Y. Hardy,
    Supersymmetric Hamilton Operator and Entanglement,
    Zeitschrift für Naturforschung, 61a, 139—140, 2006.
32. Y. Hardy, W.-H. Steeb and R. Stoop,
    Genetic Algorithms, Floating Point Numbers and Applications,
    International Journal of Modern Physics C, 16, 1811—1816, 2005.
33. W.-H. Steeb, Y. Hardy and R. Stoop,
    Bell-CHSH Inequality and Genetic Algorithms,
    Zeitschrift für Naturforschung, 60a, 865—866, 2005.
34. Y. Hardy and W.-H. Steeb,
    Fermi-Bose Systems, Macroscopic Quantum Superposition States and Entanglement,
    International Journal of Theoretical Physics, 43, 2207—2213, 2004.
35. Y. Hardy and W.-H. Steeb,
    Entanglement, Hubbard Model and Symmetries,
    International Journal of Theoretical Physics, 43, 341—347, 2004.
36. Y. Hardy, W.-H. Steeb and R. Stoop,
    Entanglement, Disentanglement and Wigner Functions,
    Physica Scripta, 69, 166—169, 2004.
37. Y. Hardy, W.-H. Steeb and R. Stoop,
    Fully Entangled Quantum States in C^N2 and Bell Measurement,
    International Journal of Theoretical Physics, 42, 2865—2872, 2003.
38. W.-H. Steeb and Y. Hardy,
    Chaotic Maps, Invariants, Bose Operators, and Coherent States,
    International Journal of Theoretical Physics, 42, 85—88, 2003.
39. W.-H. Steeb, Y. Hardy and R. Stoop,
    Lax Representation and Kronecker Product,
    Physica Scripta, 67, 464—465, 2003.
40. W.-H. Steeb, Y. Hardy and R. Stoop,
    Discrete Wavelets and Perturbation Theory,
    Journal of Physics A: Mathematical and General, 36, 6807—6811, 2003.
41. Y. Hardy and W.-H. Steeb,
    Gene Expression Programming and One-dimensional Chaotic Maps,
    International Journal of Modern Physics C, 13, 13—24, 2002.
42. W.-H. Steeb and Y. Hardy,
    Entangled Quantum States and the Kronecker Product,
    Zeitschrift für Naturforschung, 57a, 689—691, 2002.
43. W.-H. Steeb, Y. Hardy and R. Stoop,
    Discrete Wavelets and Filtering Chaotic Signals,
    International Journal of Modern Physics C, 13, 771—776, 2002.
44. Y. Hardy and W.-H. Steeb,
    Fermi Systems, Hubbard Model and a SymbolicC++ Implementation,
    International Journal of Modern Physics C, 12, 235—245, 2001.
45. W.-H. Steeb, Y. Hardy Y. and R. Stoop,
    Energy Eigenvalue Level Motion with Two Parameters,
    Zeitschrift für Naturforschung, 56a, 565—567, 2001.
46. W.-H. Steeb, Y. Hardy and R. Stoop,
    Bessel Functions, Recursion and a Nonlinear Field Equation,
    Zeitschrift für Naturforschung, 56a, 710—711, 2001.
47. Y. Hardy, W.-H. Steeb and C.M. Villet,
    Stabilization of Chaotic Systems with Phase Coupling,
    Zeitschrift für Naturforschung, 55a, 847—850, 2000.
48. W.-H. Steeb and Y. Hardy,
    Quantum Computing and SymbolicC++ Simulations,
    International Journal of Modern Physics C, 11, 323—334, 2000.
49. W.-H. Steeb and Y. Hardy,
    Entangled Quantum States and a C++ Implementation,
    International Journal of Modern Physics C, 11, 69—77, 2000.
50. Y. Hardy, W.-H. Steeb and R. Stoop,
    Jacobi Elliptic Functions, Nonlinear Evolution Equations and Recursion,
    International Journal of Modern Physics C, 11, 27—31, 2000.
51. W.-H. Steeb and Y. Hardy,
    Energy Eigenvalue Level Motion and a SymbolicC++ Implementation,
    International Journal of Modern Physics C, 11, 1347—1356, 2000.
52. W.-H. Steeb and Y. Hardy,
    Entangled Quantum States,
    International Journal of Theoretical Physics, 39, 2765—2770, 2000.
53. Y. Hardy and W.-H. Steeb,
    The Rikitake Two-Disk Dynamo System and Domains with Periodic Orbits,
    International Journal of Theoretical Physics, 38, 2413—2417, 1999.

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