Generalized Eigenvectors

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Generalized eigenvectors. Generalized eigenspaces. Generalized eigenvectors corresponding to distinct eigenvalues are linearly independent.
  1. Sheldon Axler
  2. linear algebra
  3. Linear Algebra Done Right
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Автор

the best book on linear algebra. I recommended to my students without reservation！！！！ great to know that the author has teaching videos online

wdlang
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The idea behind the linear independence proof is very nice. Can't it also be used to prove Proposition 5.10 in the book?

nairanjith
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11:06
I'm confused by this part. Operator composition is not generally commutative, so how come are we allowed to put (T - \lambda_1 I)^k in front of the rest and apply it to v_1?

mateuszbaginski
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Concepts are great, but you skipped all the actual work. You skipped the work where you actually find the Generalized eigenvectors. If T were different, how could I find the generalized eigenvectors of the new T? We also need this work, I went back into the book and I only found more concepts where the work for finding eigenvectors was skipped. Is there a way to find the eigenvectors without putting T into a matrix?

oscaralvarez
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My calculation of (T-5l)^3(z_1, z_2, z_3) ends up at (-125z_1 + 220z_2, -125z_2, 0) and I'm not sure where it's going wrong.

si_monster