Related papers: Evaluating matrix power series with the Cayley-Ham…

In this note we discuss the problem of finding the nth power of a matrix which is strongly connected to the study of Markov chains and others mathematical topics. We observe the known fact (but maybe not well known) that the Cayley-Hamilton…

A finite expansion of the exponential map for a $N\times N$ matrix is presented. The method uses the Cayley-Hamilton theorem for writing the higher matrix powers in terms of the first N-1 ones. The resulting sums over the corresponding…

We establish the analogue of the Cayley--Hamilton theorem for the quantum matrix algebras of the symplectic type.

We present two hypermatrix formulations of the Cayley Hamilton theorem. One of the proposed formulation naturally extends to hypermatrices the combinatorial interpretations of the classical Cayley Hamilton theorem. We conclude by discussing…

In this note, the first-order Dickson polynomials are introduced through a particular case of the expression of the trace of the $n^{th}$ power of a matrix in terms of powers of the trace and determinant of the matrix itself. The technique…

The classical Cayley-Hamilton identities are generalized to quantum matrix algebras of the GL(m|n) type.

The Cayley--Hamilton--Newton theorem for half-quantum matrices is proven.

We propose a modification to the Cayley transform that defines a suitable local parameterization for the special unitary group $\mathrm{SU}(3)$. The new mapping is used to construct splitting methods for separable Hamiltonian systems whose…

We report on our formalization of matrix-interpretation in Isabelle/HOL. Matrices are required to certify termination proofs and we wish to utilize them for complexity proofs, too. For the latter aim, only basic methods have already been…

We derive an improved lattice Hamiltonian for pure gauge theory, coupling arbitrarily distant links in the kinetic term. The level of improvement achieved is examined in variational calculations of the SU(2) specific heat in 2+1 dimensions.

In recent years, we have established the iteration theory of the index for symplectic matrix paths and applied it to periodic solution problems of nonlinear Hamiltonian systems. This paper is a survey on these results.

For a family of the orthogonal $O(k)$ type Quantum Matrix algebras we establish an analogue of the Cayley--Hamilton theorem. The form of the Cayley-Hamilton identity is different in three cases. First, the cases of odd ($k=2\ell -1$) and…

In this paper we show how gauge symmetries in an effective theory can be used to simplify proofs of factorization formulae in highly energetic hadronic processes. We use the soft-collinear effective theory, generalized to deal with…

Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value…

Hamiltonian matrices appear in a variety or problems in physics and engineering, mostly related to the time evolution of linear dynamical systems as for instance in ion beam optics. The time evolution is given by symplectic transfer…

For hamiltonian lattice gauge theory, we introduce the matrix product anzats inspired from density matrix renormalization group. In this method, wavefunction of the target state is assumed to be a product of finite matrices. As a result,…

In this expository paper, various properties of matrix traces, determinants and adjugate matrices are proved, including the *trace Cayley-Hamilton theorem*, which says that \[ kc_k + \sum_{i=1}^k \operatorname{Tr} (A^i) c_{k-i} = 0 \qquad…

Starting from a mistake done by a student, we discover an unexpected method of finding both eigenvectors for a $2\times2$ matrix with distinct eigenvalues in a single computation. We discuss a connection with the Cayley-Hamilton theorem,…

We develop a method to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley-Hamilton theorem for hypermatrices.

The deep interconnection between linear algebra and graph theory allows one to interpret classical matrix invariants through combinatorial structures. To each square matrix A over a commutative ring K, one can associate a weighted directed…