The eigenvectors and eigenvalues of block circulant matrices had been found for real symmetric matrices with symmetric submatrices, and for block circulant matrices with circulant submatrices. The eigenvectors are now found for general block circulant matrices, including the Jordan Canonical Form for defective eigenvectors. That analysis is applied to Stephen J. Watson’s alternating circulant m...

Current dynamical overlap fermion hybrid Monte Carlo simulations encounter large fermionic forces when there is mixing between near zero-eigenvectors of the kernel operator. This leads to low acceptance rates when there is a large density of near zero eigenvectors. I present a method where these large forces are eliminated and the large action jumps seen when two eigenvectors approach zero are ...

Eigenvectors and eigenvalues are numbers and vectors associated to square matrices, and together they provide the eigen-decomposition of a matrix which analyzes the structure of this matrix. Even though the eigen-decomposition does not exist for all square matrices, it has a particularly simple expression for a class of matrices often used in multivariate analysis such as correlation, covarianc...

The notions of asymptotic eigenvectors and asymptotic eigenvalues are defined. Based on these notions a special probability rule for pattern selection in a Hopfield type dynamics is introduced. The underlying network is considered to be a d -regular graph, where d is an integer denoting the number of nodes connected to each neuron. It is shown that as far as the degree d is less than a critical...

Some new properties of the eigenvalues of the subdirect sums are presented for the particular case of 1-subdirect sums. In particular, it is shown that if an eigenvalue λ is associated with certain blocks of matrix A or matrix B then λ is also an eigenvalue associated with the 1-subdirect sum A ⊕1 B. Some results concerning eigenvectors of the k-subdirect sum A⊕k B for an arbitrary positive int...

The partition function for the problem of an arbitrary number of directed nonintersecting walks interacting with one or two walls parallel to the direction of the walks is calculated exactly utilizing a theorem recently proved concerning the Bethe ansatz for the eigenvectors of the transfer matrix of the five-vertex model. This theorem shows that the completeness of the Bethe ansatz eigenvector...

We exploit the Laplace-Beltrami operator to represent shapes which in turn is used for designing a shape based transfer function for volume rendering. Laplace-Beltrami spectral measures are isometry invariant and are one of the most powerful ways to represent shape, also called “Shape-DNA”. Isosurfaces are extracted from the volume data and the Laplace-Beltrami operator is applied on these extr...

We exploit the Laplace-Beltrami (LB) operator to represent shapes, which in turn is used to visualize certain standard datasets specifically for biomedical applications. LB spectral measures are isometry invariant and are one of the most powerful ways to represent shape, also called “Shape-DNA”. We define a shape signature by finding the eigenvalues and eigenvectors of the LB matrix for the giv...

Motivated by the conjectures formulated in 2003 [28], we study interlacing properties of eigenvalues A⊗B+B⊗A for pairs n-by-n matrices A,B. We prove that every pair symmetric (and skew-symmetric matrices) with one them at most rank two, odd spectrum (those determined eigenvectors) interlaces its even eigenvectors). Using this result, also show when n≤3, The results specify structure eigenvector...