3D geometry exercises with linear algebra

In summary, the person is looking for a book to practice 3D geometry problems, specifically for computer vision and rigid body motion. One suggestion is "Matrix Theory for Physicists" by J. Heading, which also covers classical mechanics, E/M, QM, and SR. However, it may not include exercises for projective geometry. Another recommended book is "Projective and Analytical Geometry" by J. A. Todd, which is older than Heading's book. The author also mentions "A Vector Space Approach to Geometry" by Hausner as a potential option.
  • #1
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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  • #2
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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  • #3
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...
 
  • #4
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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  • #5
A vector space approach to geometry by Hausner maybe?
 

What is the purpose of learning 3D geometry exercises with linear algebra?

The purpose of learning 3D geometry exercises with linear algebra is to understand how to use mathematical concepts and tools to solve problems related to three-dimensional space. This includes understanding how to represent and manipulate objects in 3D space, as well as how to use linear algebra techniques to solve problems involving vectors, matrices, and transformations.

What are some common applications of 3D geometry exercises with linear algebra?

Some common applications of 3D geometry exercises with linear algebra include computer graphics, computer-aided design (CAD), robotics, and video game development. These fields often require the use of 3D geometry and linear algebra to create and manipulate objects in a virtual 3D space.

What are some key concepts to understand in 3D geometry exercises with linear algebra?

Some key concepts to understand in 3D geometry exercises with linear algebra include vectors, matrices, transformations, and coordinate systems. It is also important to understand how to perform operations such as translation, rotation, and scaling on objects in 3D space using linear algebra techniques.

How can I improve my skills in 3D geometry exercises with linear algebra?

To improve your skills in 3D geometry exercises with linear algebra, it is important to practice solving problems and working with different types of 3D objects. You can also read textbooks or watch online tutorials to gain a deeper understanding of the concepts and techniques involved.

Are there any resources available to help with learning 3D geometry exercises with linear algebra?

Yes, there are many resources available to help with learning 3D geometry exercises with linear algebra. These include textbooks, online tutorials, interactive software, and practice problems. You can also seek help from teachers, tutors, or online communities for additional support and guidance.

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