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Preliminaries on Trusses
Published in A.I. Rusakov, Fundamentals of Structural Mechanics, Dynamics, and Stability, 2020
A square matrix with a zero determinant is referred to as a singular matrix; otherwise a square matrix is called nonsingular. The determinant of matrix A is denoted as det A. The existence and uniqueness of the solution of a linear equation set is defined by whether the coefficient matrix is singular or not. The solution of the linear equation set in vector form (7I.3) exists and is unique on the obligatory condition: det A ≠ 0. It follows that for an absolute term vector b = 0 and upon the condition det A ≠ 0, the solution of equation (7I.3) is only and trivial: x = 0. If det A = 0, the solution may not exist, but if it exists, then there exists an infinite set of other solutions. Thus, for absolute term vector b = 0 upon condition det A = 0, one can find the nontrivial solution x ≠ 0.
Review of Basic Laws and Equations
Published in Pradip Majumdar, Computational Methods for Heat and Mass Transfer, 2005
A coefficient matrix is a matrix whose elements are the coefficients of the unknowns in a system of equations. For example, the coefficient matrix for the system of equations given by Equation 3.1 is A=a11a12⋯⋯⋯a1na21a22⋯⋯⋯a2n⋮⋮⋮an1an2⋯⋯⋯ann
An integrated solution for reducing ill-conditioning and testing the results in non-linear 3D similarity transformations
Published in Inverse Problems in Science and Engineering, 2018
Everywhere of the publication, the inverse of the normal equations coefficient matrix () is calculated by Pseudo Inverse Method via SVD to reduce the second type ill-conditioning (raised from the common point data sets distributed on a plane or a line).