Projections in real inner product spaces

Topic(s):

Exposition of the theory of (not necessarily orthogonal) projections. Discusses orthogonal complements, adjoints, and matrix representations. Mentions generalization to complex vector spaces.

Identifier:

http://www.math.wayne.edu/~drucker/MAALinAlgResources/projections2.pdf

Subject:

Linear Algebra

Inner Product Spaces

Rating:

Creator(s):

Daniel Drucker

Cataloger:

Steven Leon

Publisher:

Wayne State University website

Rights:

Daniel Drucker

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Comments

material is nicely presented, maybe too much for a first course

Permalink Submitted by Anonymous (not verified) on Wed, 2014-07-30 18:21

The paper consists of ten theorems which provide a nice coverage of the topic, projections in inner product spaces. It covers both orthogonal and nonorthogonal projections. I am not sure, however, how useful this material would be in a first course in linear algebra. Ten theorems is a lot to throw at the students, particularly in a course where the majority of students are likely to be majoring in fields other than mathematics. Still the material is nicely presented and could be useful for a second course in linear algebra that is designed for math majors.