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 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 ...

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: THE EQUIVALENT CIRCUIT of the iron-core transformer is usually presented as fact, with but a casual attempt at justification of the circuit configuration or the values of the parameters. It ...