The characteristic equation - Eigenvalue and Eigenvectors
The characteristic equation
Lessons
Notes:
We say that a scalar is an eigenvalue of an matrix if and only if satisfies the following characteristic equation:
We say that is a characteristic polynomial.
Useful ways to find eigenvalues
When dealing with a matrix, use the formula .
When dealing with a matrix, use the shortcut method.
When dealing with a triangular matrix, know that the determinant is just the product of the diagonal entries.
Note that:
1. An eigenvalue is a distinct root if it has a multiplicity of 1
2. An eigenvalue is a repeated root if it has a multiplicity greater than 1
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Intro Lesson
The Characteristic Equation Overview:
