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 ...

ABSTRACT: New approach to systems of polynomial recursions is developed based on the Carleman linearization procedure. The article is divided into two main sections: firstly, we focus on the case of ...

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 ...

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 ...

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 ...

The RREF of a given matrix is computed using the standard cubic runtime algorithm (O(n^3)), wherein each diagonal is attempted to form a pivot, and entries below and above that pivot are reduced to ...