6 Answered Questions for the topic eigenvalues eigenvectors

Eigenvalues Eigenvectors Linear Algebra Polynomials Matrices

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... more
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Eigenvalues Eigenvectors Linear Algebra Matrices Abstract Algebra

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... more
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Eigenvalues Eigenvectors Linear Algebra Matrices

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... more
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Eigenvalues Eigenvectors Linear Algebra Matrices

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.... more
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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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Eigenvalues Eigenvectors Linear Algebra Matrix Rank

03/19/19

What is the relation between rank of a matrix, its eigenvalues and eigenvectors?
I am quite confused about this. I know that zero eigenvalue means that null space has non zero dimension. And that the rank of matrix is not the whole space. But is the number of distinct... more
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