Eigenvalues and eigenvectors - Eigenvalue and Eigenvectors
Eigenvalues and eigenvectors
Lessons
Notes:
An eigenvector of an matrix is a non-zero vector such that , for some scalar . The scalar is called the eigenvalue.
We say the eigenvector corresponds to the eigenvalue .
Given an eigenvalue of matrix , we can find a corresponding eigenvector by solving
And finding a non-trivial solution .
The eigenspace is the null space of the matrix . In other words, the eigenspace is a set of all solutions for the equation
Of course, we can find the basis for the eigenspace by finding the basis of the null space of .
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Intro Lesson
Eigenvalues and Eigenvectors Overview:
