In the paper, the authors establish two identities to express higher order derivatives and integer powers of the generating function of the Chebyshev polynomials of the second kind in terms of integer ...

Drazin inverses and their modern generalisations constitute a pivotal area of operator theory within Banach algebras. These inverse concepts extend the classic notion of the matrix inverse to settings ...

Dr. James McCaffrey of Microsoft Research guides you through a full-code, step-by-step tutorial on "one of the most important operations in machine learning." Computing the inverse of a matrix is one ...

Let Λ and Γ be Artin algebras, M a Γ-Λ-bimodule, and R the triangular matrix ring of Λ, Γ, and M; assume that R is also an Artin algebra. The R-modules are triples (U, V, f) where U is a Λ-module, V ...

For a symmetric correlation matrix, the Inverse Correlation Matrix table contains the inverse of the correlation matrix, as shown in Figure 40.14. The diagonal elements of the inverse correlation ...

Compared to FSDT-based inverse elements, iKS3 exhibits improved numerical stability and faster convergence, even under complex loading conditions. Validation studies conducted under in-plane, ...