4 citations · 16 across the 21 of their papers we have counts for
21 papers
Canonical forms for boundary conditions of self-adjoint odd-order differential operators
Yorick Hardy, Bertin Zinsou
It is useful to have canonical forms of boundary conditions in the study of the eigenvalues of boundary value problems and associated numerical applications. In [J. Appl. Anal. Com…
Kronecker differences
Keegan Doig Anderson, Yorick Hardy, Bertin Zinsou
Over the real numbers, the Kronecker sum is the unique operation on matrices which exponentiates to the Kronecker product. Kronecker quotients provide an algebraic view of decompos…
Canonical forms for boundary conditions of self-adjoint differential operators
Yorick Hardy, Bertin Zinsou
Canonical forms of boundary conditions are important in the study of the eigenvalues of boundary conditions and their numerical computations. The known canonical forms for self-adj…
Preserving the trace of the Kronecker sum
Yorick Hardy, Ajda Fošner
The aim of this paper is to study linear preservers of the trace of Kronecker sums and their connection with preservers of determinants of Kronecker products. The partial trace and…
Partial determinants of Kronecker products
Yorick Hardy
Let be the block-wise determinant (partial determinant). We consider the condition for completing the determinant and characterize the case…
Matrices, Fermi Operators and Applications
Yorick Hardy, Willi-Hans Steeb, Garreth Kemp
We consider the vector space of matrices over , Fermi operators and operators constructed from these matrices and Fermi operators. The properties of these o…
Bose Operators, Coherent States, Truncation, Spin Coherent States, Lie Algebras and Spectrum
Willi-Hans Steeb, Garreth Kemp, Yorick Hardy +1
We study truncated Bose operators in finite dimensional Hilbert spaces. Spin coherent states for the truncated Bose operators and canonical coherent states for Bose operators are c…
Hierarchy of Spin Operators, Quantum Gates, Entanglement, Tensor Product and Eigenvalues
Willi-Hans Steeb, Yorick Hardy
{\bf Abstract.} We show that two hierarchies of spin Hamilton operators admit the same spectrum. Both Hamilton operators play a central role for quantum gates in particular for the…
A Short Note on Kronecker Square Roots
Yorick Hardy
The results of [I. Ojeda, Amer. Math. Monthly, 122, pp 60--64] provides a characterization of Kronecker square roots of matrices in terms of the symmetry and rank of the block vec…
Spin Operators, Pauli Group, Commutators, Anti-Commutators, Kronecker Product and Applications
Willi-Hans Steeb, Yorick Hardy
Pauli spin matrices, Pauli group, commutators, anti-commutators and the Kronecker product are studied. Applications to eigenvalue problems, exponential functions of such matrices,…
On Kronecker Quotients
Yorick Hardy
Leopardi introduced the notion of a Kronecker quotient in [Paul Leopardi. A generalized FFT for Clifford algebras. Bulletin of the Belgian Mathematical Society, 11:663--688, 2005.]…
Boolean Functions, Quantum Gates, Hamilton Operators, Spin Systems and Computer Algebra
Yorick Hardy, Willi-Hans Steeb
We describe the construction of quantum gates (unitary operators) from boolean functions and give a number of applications. Both non-reversible and reversible boolean functions are…
Exponential of a Matrix, a Nonlinear Problem and Quantum Gates
Willi-Hans Steeb, Yorick Hardy
We describe solutions of the matrix equation , where . Applications in quantum computing are given. Both normal and nonnormal matrices are stud…
Majorana Fermions on a Lattice and a Matrix Problem
Yorick Hardy, Willi-Hans Steeb
We investigate matrix problems arising in the study of Majorana Fermions on a lattice.
Cayley transform and the Kronecker product of Hermitian matrices
Yorick Hardy, Ajda Fošner, Willi-Hans Steeb
We consider the conditions under which the Cayley transform of the Kronecker product of two Hermitian matrices can be again presented as a Kronecker product of two matrices and, if…
An Eigenvalue Problem for a Fermi System and Lie Algebras
Willi-Hans Steeb, Yorick Hardy
We study a Fermi Hamilton operator which does not commute with the number operator . The eigenvalue problem and the Schrödinger equation is solved. Entanglement is…
Exceptional Points, Nonnormal Matrices, Hierarchy of Spin Matrices and an Eigenvalue Problem
Willi-Hans Steeb, Yorick Hardy
Exceptional points of a class of non-hermitian Hamilton operators of the form are studied, where and are hermitian operat…
Spin-Hamilton Operator, Graviton-Photon Coupling and an Eigenvalue Problem
Yorick Hardy, Willi-Hans Steeb
We solve exactly the eigenvalue problem for a spin Hamilton operator describing graviton-photon coupling. Entanglement of the eigenstates are also studied. Other spin-coupled Hamil…
Hamilton Operators, Discrete Symmetries, Brute Force and SymbolicC++
Willi-Hans Steeb, Yorick Hardy
To find the discrete symmetries of a Hamilton operator is of central importance in quantum theory. Here we describe and implement a brute force method to determine the dis…
A Sequence of Quantum Gates
Yorick Hardy, Willi-Hans Steeb
We study a sequence of quantum gates in finite-dimensional Hilbert spaces given by the normalized eigenvectors of the unitary operators. The corresponding sequence of the Hamilton…
Spin Hamilton Operators, Symmetry Breaking, Energy Level Crossing and Entanglement
Willi-Hans Steeb, Yorick Hardy, Jacqueline de Greef
We study finite-dimensional product Hilbert spaces, coupled spin systems, entanglement and energy level crossing. The Hamilton operators are based on the Pauli group. We show that…