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 ...

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 ...

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: The article contains description of the major types of convolutions and algebra of multidimensional matrices. It is shown that all major types of convolutions have been expressed in terms of ...