Lecture 23
University of Arizona
INFO 511 - Fall 2024
- Eigenvalues and eigenvectors decompose a matrix into its fundamental components.
- Eigenvalue equation: Av=λv
We will be using Python for this…
Decomposition formula: A=QLQ−1
Q is the matrix of eigenvectors, L is the diagonal matrix of eigenvalues, and Q−1 is the inverse of Q
Principal Component Analysis (PCA): Reduces dimensionality while preserving variance.
Eigenvalues in system stability: Determine stability in control systems and differential equations.
Identity Matrix: Diagonal of 1s, other elements are 0s.
I=[100010001]
Diagonal Matrix: Non-zero elements only on the diagonal.
D=[400050006]
Triangular Matrix: Triangular shape of non-zero elements (upper U, lower L).
U=[123045006]L=[100230456]
ae-16-pcaPrincipal Component Analysis
