For a square matrix ( A ), an eigenvalue ( \lambda ) and a corresponding eigenvector ( v ) are defined by the equation: [ Av = \lambda v ] The eigenvalue ( \lambda ) is a scalar that scales the ...

In this paper, we obtain a formula for the derivative of a determinant with respect to an eigenvalue in the modified Cholesky decomposition of a symmetric matrix, a characteristic example of a direct ...

Introduces linear algebra and matrices, with an emphasis on applications, including methods to solve systems of linear algebraic and linear ordinary differential equations. Discusses computational ...

In this paper, a series of bicomplex representation methods of quaternion division algebra is introduced. We present a new multiplication concept of quaternion matrices, a new determinant concept, a ...

This repository presents a deep dive into linear algebra, illustrating a collection of pivotal concepts, algorithms, and applications. It presents the a wide range of the mathematical techniques and ...

Abstract: Several methods of solving the algebraic Riccati equation (ARE) are presented. Functional iterations with acceleration techniques am introduced. Also variations of the Newton method, the ...

Abstract: Resilience is an important research topic in HPC. As computer clusters go to extreme scales, work in this area is necessary to keep these machines reliable. In this work, we introduce a ...