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Pseudoinverse

Discusses the pseudoinverse in the context of least squares problems. Properties of pseudoinverse and formulas for its calculation. Relates pseudoinverse to singular value decomposition.

Identifier: 
http://www.math.wayne.edu/~drucker/MAALinAlgResources/pseudoinverse2.pdf
Subject: 
Rating: 
Average: 4 (2 votes)
Creator(s): 
Daniel Drucker, partially based on material from an early edition of Strang's "Linear Algebra and Its Applications"
Cataloger: 
Steven Leon
Publisher: 
Daniel Drucker
Rights: 
Daniel Drucker, partially based on material from an early edition of Strang's "Linear Algebra and Its Applications"

Comments

Anonymous's picture

These pages present a nice discussion of least squares and the pseudoinverse. Most linear algebra textbooks that discuss the pseudoinverse use the singular value decomposition (svd) to derive a way of computing the pseudoinvers of a matrix. Unfortunately, the majority of linear algebra courses never get around to doing the svd as there is just too much important material to fit into a single course. In this paper the authors derives the pseudoinverse from an LU factorization of the nonsquare matrix A. This is a different approach from most textbooks and it allows the instructor to cover the topic of pseudoinverse without doing svd first. It should be noted that the paper also does do the svd derivation of the pseudoinverse. Least squares is a standard topic that is covered in the first course in linear algebra and using the approach shown in this paper it should be possible to now use the pseudoinverse to cover rank deficient least squares problems. The paper is a helpful tool in teaching least squares problems. The paper would be even more accessible to students if the author were to add some worked out examples.

meade's picture

This is a very thorough, but dense, derivation of the pseudoinverse. Well written, but probably overly general for most students to fully comprehend. Instructors, however, should find it quite useful.

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