Linear Transformation and Diagonalization Problem

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Homework Help Overview

The discussion revolves around a problem related to linear transformations and diagonalization, specifically focusing on the characteristic polynomial and the implications of complex eigenvalues.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the characteristic polynomial of a matrix and its implications for diagonalization, particularly in cases involving complex eigenvalues.

Discussion Status

There appears to be a consensus on the form of the characteristic polynomial, with some participants confirming its correctness. The implications of having complex eigenvalues and the resulting non-diagonalizability over the reals are also being explored.

Contextual Notes

Participants are considering the constraints of diagonalization in relation to the nature of the eigenvalues, particularly in the context of real versus complex numbers.

Stapler2000
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Nevermind -- Polygons and Polywags.
 
Last edited:
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matrix in standard basis looks good, but i would check your characteristic polynomial
 
i got x^2 - x + 6 = 0
 
however as you mention it is correct that in the case T has complex eigenvalues it is not diagonalisable over the reals
 
Agreed -- it is x^2-x+6.
 

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