Which Books Can Help Clarify Chapter 3 of Linear Algebra in Boas?

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Discussion Overview

The discussion revolves around the clarity of Chapter 3 on Linear Algebra in the book by Boas. Participants are seeking recommendations for alternative texts that may provide clearer explanations of concepts related to linear algebra, particularly in the context of vectors, distances between planes, and matrices.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant expresses difficulty in understanding certain areas of Chapter 3 in Boas, particularly regarding the use of vectors and the identification of perpendicular vectors to planes.
  • Another participant recommends 'A Survey of Modern Algebra' by Birkhoff and Mac Lane as a resource for clearer treatment of linear algebra concepts.
  • Concerns are raised about the clarity of topics such as distances between lines and planes, parametric equations, and the depth of coverage on matrices in Boas' text.
  • A suggestion is made to consult Stewart's calculus book for additional insights on vectors, along with recommendations for books focused specifically on matrix algebra.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on a single alternative text, and multiple suggestions are offered, indicating a variety of perspectives on which resources may be helpful.

Contextual Notes

Participants mention specific areas of confusion, such as the identification of perpendicular vectors and the treatment of matrices, but do not resolve these issues or clarify the assumptions underlying their difficulties.

Who May Find This Useful

Readers interested in linear algebra, particularly those seeking clearer explanations of vectors, distances, and matrices, may find the recommendations and discussions beneficial.

WiFO215
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I find that Chapter 3(Linear Algebra) in Boas is not very clear in certain areas. Could someone please recommend a book which does so more clearly?
 
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'A Survey of Modern Algebra' by Garrett Birkhoff and Saunders Mac Lane has a really good treatment of linear algebra. Anything particular that you didn't find clear in Boas' treatment, or the whole topic of linear algebra?
 
She uses vectors to find distances between planes and such. Example given a plane 3x + 4y + 5z she immediately says the vector perpendicular to this plane is such and such. I don't know how she gets that.

Distance between lines, planes, parametric equations et. al. are not too clear.

Matrices could have been done with a little more depth. The different types of matrices are over in a flash.
 

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