A note on pseudo-inverse

Kai Ming Yu

Research output: Journal article publicationJournal articleAcademic researchpeer-review


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.
Original languageEnglish
Pages (from-to)309-314
Number of pages6
JournalInternational Journal of Engineering Education
Issue number4
Publication statusPublished - 1 Dec 1996

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Education


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