Proving A & AT Share Same Eigenvalue

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    Eigenvalue
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Homework Help Overview

The discussion revolves around proving that a matrix \( A \) and its transpose \( A^T \) share the same eigenvalue. Participants are exploring the properties of eigenvalues and eigenvectors in the context of linear algebra.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to understand the relationship between eigenvalues of \( A \) and \( A^T \), with some exploring the implications of transposing eigenvectors and matrices. Questions arise regarding the steps taken in reasoning, particularly concerning the properties of transposition and the definitions of eigenvalues.

Discussion Status

The discussion is active, with various participants questioning assumptions and clarifying points about matrix properties and eigenvalues. Some have suggested different approaches to the proof, while others express uncertainty about the implications of their reasoning.

Contextual Notes

There are mentions of constraints related to the participants' familiarity with certain mathematical concepts, such as determinants and inner products, which may affect their ability to engage fully with the problem. Additionally, the discussion includes references to specific cases of matrices that may influence the proof structure.

  • #31
Dick said:
Donald Knuth. "The Art of Computer Programming". And it is art. He wrote TeX. Shame, and more shame on CS if you don't know him. No, I don't teach anything. I failed to get into academia, so I sit around all day writing engineering software and looking for interesting problems to work on. Go figure. Check out Knuth, you'll like it with your inclinations.

I'll give him a try, thanks a bunch! From your posts, I'm surprised you
failed to get into academia.
 
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  • #32
evilpostingmong said:
I'll give him a try, thanks a bunch! From your posts, I'm surprised you
failed to get into academia.

You try it. See how you do. Let me know.
 

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