You are already quite familiar with the linear form of a matrix. The *linear form of a matrix* is simply a linear mapping of that matrix. In scalar algebraic notation, we might write: f(x) = a_1x_1 + ...

Abstract: In this correspondence, the densities of quadratic forms on complex random matrices and their joint eigenvalue densities are derived for applications to information theory. These densities ...

Several areas of regression analysis involve the evaluation of quadratic forms of the matrix (X'X)-1. This article draws these areas together and shows how a technique due to Salkever (1976) can be ...

The paper provides significant simplifications and extensions of results obtained by Gorsich, Genton, and Strang (J. Multivariate Anal. 80 (2002) 138) on the structure of spatial design matrices.

This is an (unfinished) algorithm of diagonalization of quadratic form matrices. Intented as an exercice larening about bilinear and quadratic forms in an algebra course. The program can diagonalize ...

Consider a mapping $F: \mathbf{R}^n \rightarrow \mathbf{R}^3 (n \geqslant 3)$ defined by an ordered triple of real-valued quadratic forms; if some linear combination ...

Abstract: We design static anti-windup gains to mitigate the effect of input saturation in linear output feedback closed loops. The design is conducted with the help of a non-quadratic Lyapunov ...

The current attempt is aimed to extend previous results, concerning the explicit expression of the arithmetic mean standard deviation distribution, to the general case of the weighted mean standard ...

Conway’s topograph provided a combinatorial-geometric perspective on integer binary quadratic forms—quadratic functions of two variables with integer coefficients. This perspective is practical for ...