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2003•College MathematiesRequires access

On the Confirmation of the Eigenvalues and the Eigenvectors of Matrix

Shi Jin-song

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Abstract

We summed up the conclusions of finding the eigenvalues and the eigenvectors of A~(-1), (transpose) matrix A~T, adjoint matrix A~*,P~(-1)AP and polynomial φ(A) from the eigenvalues and the eigenvectors of A at first. Then, some results of rightabout are presented. At last, we discussed how we could determine the eigenvalues and the eigenvectors of A from the eigenvalues and the eigenvectors of φ(A) via some examples.

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What this paper is about

We summed up the conclusions of finding the eigenvalues and the eigenvectors of A~(-1), (transpose) matrix A~T, adjoint matrix A~*,P~(-1)AP and polynomial φ(A) from the eigenvalues and the eigenvectors of A at first. Then, some results of rightabout are presented. At last, we discussed how we could determine the eigenvalues and the eigenvectors of A from the eigenvalues and the eigenvectors of φ(A) via some examples.

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Available abstract

We summed up the conclusions of finding the eigenvalues and the eigenvectors of A~(-1), (transpose) matrix A~T, adjoint matrix A~*,P~(-1)AP and polynomial φ(A) from the eigenvalues and the eigenvectors of A at first. Then, some results of rightabout are presented. At last, we discussed how we could determine the eigenvalues and the eigenvectors of A from the eigenvalues and the eigenvectors of φ(A) via some examples.

Key concepts: Eigenvalues and eigenvectors, Eigenvalues and eigenvectors of the second derivative, Defective matrix, Matrix differential equation, Eigenvalue perturbation, Modal matrix, Mathematics, Spectrum of a matrix

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