5 Answered Questions for the topic eigenvalues eigenvectors

Eigenvalues Eigenvectors Linear Algebra Polynomials Matrices


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... more
Eigenvalues Eigenvectors Linear Algebra Matrices Abstract Algebra


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... more
Eigenvalues Eigenvectors Linear Algebra Matrices


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... more
Eigenvalues Eigenvectors Linear Algebra Matrices


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.... more
Eigenvalues Eigenvectors Linear Algebra


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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