PPT06 - Eigenvalues and Eigenvectors
PPT06 - Eigenvalues and Eigenvectors
PPT06 - Eigenvalues and Eigenvectors
Week 6
1
1
Determine eigenvalues and
eigenvectors
2 2
Diagonalization
.
Eigenvalue and Eigenvector
In this lesson, we study about eigenvalue,
eigenvector and diagonalization
Definition
If A is an
=
for some scalar , the scalar is called an eigenvalue of A and x is said to be an
eigenvector corresponding to .
Theorem
If A is an , is an eigenvalue of A if and only if it satisfies the equation
these eigenvectors are the nonzero vectors in the null space of the matrix .
Since
I, then