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Differential Equations, Lecture 4.2: Eigenvalues and eigenvectors
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Differential Equations, Lecture 4.2: Eigenvalues and eigenvectors.
An eigenvector of a square matrix is a vector v such that Av=λv, for some scalar λ called the eigenvalue. The eigenvalues of a 2x2 matrix are the roots of a degree-2 polynomial called the "characteristic polynomial". In this lecture, we learn how to find this polynomial and we analyze three examples: when the roots are real, complex, and repeated.
An eigenvector of a square matrix is a vector v such that Av=λv, for some scalar λ called the eigenvalue. The eigenvalues of a 2x2 matrix are the roots of a degree-2 polynomial called the "characteristic polynomial". In this lecture, we learn how to find this polynomial and we analyze three examples: when the roots are real, complex, and repeated.
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