Undergraduate engineering mathematical courses oftentimes emphasize algorithms leading to solutions of particular problems. One such algorithm that is implemented aims to obtain solutions for a linear system of equations. The mathematical background addressing properly constrained, under-constrained and over-constrained conditions may not be studied in depth with respect to how these situations effect their respective solutions. As an example we consider the solutions of non-homogeneous systems where the number of equations can exceed or equal or is less than the number of unknowns. The three cases will be discussed in detail for the homogeneous and non-homogeneous systems. The pseudo-inverse for a matrix will be introduced and implemented extensively to solve the non-homogeneous system. Two principle applications of the pseudo-inverse will be developed. First, we will compute the conversion matrix for Euler operators implemented in geometric modelling: secondly, will be an alternate proof for the least square error property.
|Number of pages||6|
|Journal||International Journal of Engineering Education|
|Publication status||Published - 1 Dec 1996|
ASJC Scopus subject areas
- Engineering (miscellaneous)