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Eigenvector - Coggle Diagram
Eigenvector
Branch 2
1: Start with matrix AA.
Step 2: Find the characteristic equation:
det(A−λI)\=0\det(A-\lambda I)=0
3: Solve for λ\lambda.
These values are the eigenvalues.
4: For each eigenvalue, solve:
(A−λI)v\=0(A-\lambda I)v=0
5: The non-zero solutions are the eigenvectors.
Branch 3
The vector's direction stays the same.
It can be stretched.
It can be shrunk.
It can be reversed if the eigenvalue is negative.
There is no rotation away from its eigenvector direction.
Branch 1
A non-zero vector whose direction stays the same after a matrix transformation.
Equation:
Av\=λvAv=\lambda v
Eigenvalue
The number λ\lambda that tells how much the eigenvector is scaled.
It can stretch, shrink, or reverse the vector.
Branch 4 answer (1/-1)