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 ...

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 project focuses on solving systems of linear equations using numerical methods, specifically the LU decomposition method and Gaussian elimination with pivoting. The project is implemented in ...

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 ...

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 ...

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

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 ...