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I realize that Axler's Linear Algebra Done Right is a great textbook, and the removal of determinants is often pedagogically sound. However, I was doing some problems on a practice entrance exam, and I was surprised by the amount of times solutions would involve having to apply determinants to geometric situations.

Therefore, my question is this: Where I can learn more about determinants, preferably without having to relearn all of linear algebra from another textbook?

John Clever
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  • Neil Strickland, Linear mathematics for applications (Appendix B and Section 12) does the most important proofs really well. From there I'd move on to Prasolov (Chapter I) and Krattenthaler. – darij grinberg Dec 16 '20 at 12:16
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    Actually, you can learn a lot here at this site, just search after "determinants mathematics stackexchange". For example, one of the hits for me was this nice post. I believe that there are several other interesting posts for you here, if you take the time to look them up. – Dietrich Burde Dec 16 '20 at 12:24
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    You can just keep reading Axler. Chapter 10, and specifically section 10B, is about the determinant. It will be much more productive to see the construction of the determinant "done right" and formally than go back to an introductory material now that you already have the Linear Algebraic baggage. Axler has some "applications" (if you want to call them that) of determinatns to volumes, for example, at the end of the chapter, and also connections with positive operators (which relate to calculus), etc. – Luiz Cordeiro Dec 16 '20 at 12:37

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For an easy introduction to determinants there are a lot of online resources. See for example

  1. Very basic intro to determinant

  2. Another intro to determinant with graphical representation

For a very nice graphic representation have a look at this youtube video.

Hope this helps!

Apprentice
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