5 Answered Questions for the topic eigenvalues eigenvectors

05/22/19

#### Minimal polynomials and characteristic polynomials?

I am trying to understand the similarities and differences between the minimal polynomial and characteristic polynomial of Matrices.
1. When are the minimal polynomial and characteristic...
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05/02/19

#### Must eigenvalues be numbers?

This is more a conceptual question than any other kind. As far as I know, one can define matrices over arbitrary fields, and so do linear algebra in different settings than in the typical...
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04/20/19

#### orthogonal eigenvectors?

I have a very simple question that can be stated without proof. Are all eigenvectors, of any matrix, always orthogonal? I am trying to understand Principal components and it is cruucial for me to...
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04/12/19

#### Do all square matrices have eigenvectors?

I came across a video lecture in which the professor stated that there may or may not be any eigenvectors for a given linear transformation. And, so far I thought every matrix has eigenvectors....
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Eigenvalues Eigenvectors Linear Algebra

03/27/19

#### How to prove that eigenvectors from different eigenvalues are linearly independent?

How can I prove that if I have $n$ eigenvectors from different eigenvalues, they are all linearly independent?

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