Related papers: Block-diagonalisation of matrices and operators

An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…

Let $k$ be an algebraically closed field and $\alpha$, $\beta$, $\gamma$ be partitions. An algebraic group acts on the constructible set of short exact sequences of nilpotent $k$-linear operators of Jordan types $\alpha$, $\beta$, and…

We consider a class of block operator matrices arising in the study of scattering passive systems, especially in the context of boundary control problems. We prove that these block operator matrices are indeed a subclass of block operator…

We study a class of holomorphic matrix models. The integrals are taken over middle dimensional cycles in the space of complex square matrices. As the size of the matrices tends to infinity, the distribution of eigenvalues is given by a…

In a frequency selective slow-fading channel in a MIMO system, the channel matrix is of the form of a block matrix. This paper proposes a method to calculate the limit of the eigenvalue distribution of block matrices if the size of the…

We give conditions for local diagonalization of an analytic operator family to a diagonal operator polynomial. The families are acting between real or complex Banach spaces. The basic assumption is given by stabilization of the Jordan…

Block2 is an open source framework to implement and perform density matrix renormalization group and matrix product state algorithms. Out-of-the-box it supports the eigenstate, time-dependent, response, and finite-temperature algorithms. In…

Quantum signal processing combined with quantum eigenvalue transformation has recently emerged as a unifying framework for several quantum algorithms. In its standard form, it consists of two separate routines: block encoding, which encodes…

We consider a symmetric block operator spectral problem with two spectral parameters. Under some reasonable restrictions, we state localisation theorems for the pair-eigenvalues and discuss relations to a class of non-self-adjoint spectral…

Let E be an operator algebra on a Hilbert space with finite-dimensional generated C*-algebra. A classification is given of the locally finite algebras and the operator algebras obtained as limits of direct sums of matrix algebras over E…

We give a Riemann-Hilbert approach to the theory of matrix orthogonal polynomials. We will focus on the algebraic aspects of the problem, obtaining difference and differential relations satisfied by the corresponding orthogonal polynomials.…

We present a fast algorithm for linear least squares problems governed by hierarchically block separable (HBS) matrices. Such matrices are generally dense but data-sparse and can describe many important operators including those derived…

Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…

We give sufficient conditions on a matrix A ensuring the existence of a partition of this matrix into two submatrices with extremely small norm of the image of any vector. Under some weak conditions on a matrix A we obtain a partition of A…

This article has two interpenetrating motifs. One is an exposition of some major ideas and techniques behind the use of block matrices, and especially their positivity properties. This is done by focussing on one major problem:…

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…

We study the representation theory of the cyclotomic Brauer algebra via truncation to idempotent subalgebras which are isomorphic to a product of walled and classical Brauer algebras. In particular, we determine the block structure and…

An arbitrary Mueller matrix can be decomposed into a sum of up to four deterministic Mueller-Jones matrices, with strengths given by the eigenvalues of an associated Hermitian matrix. A geometrical representation of the eigenvalues in terms…

Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on $m$-columns of half-densities on a closed manifold $M$, whose principal symbol is assumed to have simple eigenvalues. Relying on a basis of pseudodifferential…

In recent years more and more involved block structures appeared in the literature in the context of numerical approximations of complex infinite dimensional operators modeling real-world applications. In various settings, thanks the theory…