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: For a two-hop linear non-regenerative multiple-input multiple-output (MIMO) relay system where the direct link between source and destination is negligible, the optimal design of the source ...

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 ...

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 ...

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 ...

Properties of the real numbers, infimum and supremum of sets. Numerical sequences and series. Limits of functions, continuous functions, intermediate value theorem, uniform continuity. Differentiation ...