3D geometry exercises with linear algebra

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Discussion Overview

The discussion revolves around finding resources for practicing 3D geometry problems using linear algebra, particularly in the context of applications like computer vision and rigid body motion.

Discussion Character

  • Exploratory, Homework-related

Main Points Raised

  • One participant expresses a need for practice in applying linear algebra to geometric problems and seeks book recommendations.
  • Another participant suggests "Matrix Theory for Physicists" by J. Heading, noting its discussion of applications to geometry and classical mechanics.
  • A later reply questions the usefulness of Heading's book for computer vision, specifically regarding the inclusion of exercises for projective geometry.
  • Another participant recommends additional reading of "Projective and Analytical Geometry" by J. A. Todd, suggesting it may be older than Heading's work but potentially useful.
  • Another suggestion is made for "A Vector Space Approach to Geometry" by Hausner.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the best resource for practicing 3D geometry problems, and multiple competing views regarding the suitability of the suggested books remain.

Contextual Notes

Some participants express uncertainty about the applicability of the recommended books to specific areas like computer vision and projective geometry, indicating a potential limitation in the resources discussed.

Avatrin
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Hi

I have noticed that while I have the grasp of the theoretical underpinnings of linear algebra, I need work on applying it to geometric problems (think computer vision and rigid body motion). So, I am looking for a book that allows me to practice 3D geometry problems.

Is there any obvious book you guys can recommend?
 
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This is a really old book "Matrix Theory for Physicists" by J. Heading (1958) but it discusses application to geometry and classical mechanics as well as E/M, QM and SR.
 
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gleem said:
This is a really old book "Matrix Theory for Physicists" by J. Heading (1958) but it discusses application to geometry and classical mechanics as well as E/M, QM and SR.

Alright, that sounds great, but will it be useful for computer vision? I guess it doesn't include any exercises for projective geometry...
 
The author recommended additional reading of J. A. Todd "Projective and Analytical Geometry" Probably older than Heading's. Heading probably did not have computer applications in mind when he wrote his book. It does not mean that there is nothing useful or applicable to projective geometry though.
 
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A vector space approach to geometry by Hausner maybe?
 

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