This chapter is concerned with the so-called \emph{diagonalization problem}. For a given linear operator \(\T\) on a \emph{finite}-dimensional vector space \(\V\), we ...

The problem of joint approximate diagonalization of symmetric real matrices is addressed. It is reduced to an optimization problem with the restriction that the matrix of the similarity transformation ...

The task involves writing a function that accepts a square matrix and returns its eigenvalues and eigenvectors using the NumPy library. It also verifies the equality A * v = λ * v for each eigenvalue ...

Abstract: In this technical note, a general transformation for block-diagonalization (decoupling) of multitime-scale singularly perturbed linear systems composed of N subsystems is presented. The ...

This course provides an introduction to linear algebra in Euclidean space. Topics covered include: N-dimensional vectors, dot product, matrices and matrix operations, systems of linear equations and ...

Department of Cyber-Physical Systems, Clark Atlanta University, Atlanta, GA, USA. where P is some reflection (symmetric signed permutation) matrix. Like U, the generalized reflexive matrices A arise ...

Lines and Planes, The Geometry and Algebra of vectors, Systems of linear equations, Matrix algebra, Linear independence, Linear transformations, Determinants, Complex numbers, Eigenvalues, ...

Abstract: The most important linear precoding method for frequency-flat MIMO broadcast channels is block diagonalization (BD) which, under certain conditions, attains the same nonlinear dirty paper ...