Eigenvalue

Creator
Creator
Seonglae Cho
Created
Created
2022 Jan 23 13:56
Editor
Edited
Edited
2025 May 20 17:57
Refs
Refs
Each eigenvalue λ\lambda is associated with a specific eigenvector x\vec{x} for A
Ax=λxA\vec{x} = \lambda\vec{x}
Eigenvalue show how much eigenvector change to the direction
As eigenvalues decrease, the magnitude of the inverse matrix increases (inverse relationship with eigenvalues). However, when eigenvalues approach 0, the inverse matrix becomes very large, making calculations unstable.
https://github.com/kenjihiranabe/The-Art-of-Linear-Algebra

How to get eigenvalue

Hx=λx(HλI)x=0Hx=\lambda x \\ (H-\lambda I)x = 0
if there is
Eigenvector
except x=0x=0, prior should be
Singular matrix
which means
Determinant
is 0.
 
 
 
 
 
 

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