Related papers: Numerical diagonalization of fermion mass matrices
It is shown that a fermion mass matrix changing in orientation (rotating) with changing scales can give a simple yet near-quantitative explanation for quark mixing, neutrino oscillations and the fermion mass hierarchy.
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
We study the renormalization of normal mixing matrices, which includes hermitian and unitary matrices as particular cases. We give a minimal, multiplicative parametrization of counterterms, and compute the renormalized Lagrangian to…
The observed pattern of neutrino mass splittings and mixing angles indicates that their family structure is significantly different from that of the charged fermions. We investigate the implications of these data for the fermion mass…
Simultaneous matrix diagonalization is used as a subroutine in many machine learning problems, including blind source separation and paramater estimation in latent variable models. Here, we extend algorithms for performing joint…
Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…
Although a good portion of elementary linear algebra concerns itself with matrices over a field such as $\mathbb{R}$ or $\mathbb{C}$, many combinatorial problems naturally surface when we instead work with matrices over a finite field. As…
Contents: 1. Introduction 2. Fermion masses and mixing 3. Neutrino masses in the effective theory 4. Quantum corrections from the renormalization group evolution 4.1. RG equations for the CKM matrix 4.2. RG equations for neutrino masses and…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…
In a recent paper, a new method was proposed to find the common invariant subspaces of a set of matrices. This paper invstigates the more general problem of putting a set of matrices into block triangular or block-diagonal form…
Matrix completion is one of the key problems in signal processing and machine learning. In recent years, deep-learning-based models have achieved state-of-the-art results in matrix completion. Nevertheless, they suffer from two drawbacks:…
We provide a solution to the problem of simultaneous $diagonalization$ $via$ $congruence$ of a given set of $m$ complex symmetric $n\times n$ matrices $\{A_{1},\ldots,A_{m}\}$, by showing that it can be reduced to a possibly…
The analysis of diagonalizable matrices in terms of their so-called isospectral reduction represents a versatile approach to the underlying eigenvalue problem. Starting from a symmetry of the isospectral reduction, we show in the present…
A four-parameter Majorana neutrino mass matrix is proposed, which is exactly diagonalizable with two mixing angles, one of which is pi/4 and the other large but less than pi/4. The form of this mass matrix allows seven realizations of the…
This paper proposes a novel matrix rank-one decomposition for quaternion Hermitian matrices, which admits a stronger property than the previous results in (sturm2003cones,huang2007complex,ai2011new). The enhanced property can be used to…
The eigenvalue problem plays a central role in linear algebra and its applications in control and optimization methods. In particular, many matrix decompositions rely upon computation of eigenvalue-eigenvector pairs, such as diagonal or…
This paper presents the forward and backward derivatives of partial eigendecomposition, i.e. where it only obtains some of the eigenpairs, of a real symmetric matrix for degenerate cases. The numerical calculation of forward and backward…
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…
The capability of discretization of matrix elements in the problem of quadratic functional minimization with linear member built on matrix in N-dimensional configuration space with discrete coordinates is researched. It is shown, that…
Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive for high-dimensional problems. Iterative random sparsification methods allow for the estimation of a single dominant eigenvalue at reduced cost by…