Linear Algebra

• Applications
  • Linear Dynamical Systems
  • LQR Control
  • Kalman Filters
  • Probability
  • Quantum Mechanics
  • Least Squares Optimization
  • Boundary Value Problems
  • Filtering
• Matrices
  • Kronecker products
• Numerical
• Decompositions
  • LU
  • SVD
  • Jordan
  • QR
  • Eigenvector
    • Power method
    • Krylov
    • Conjugate Gradient
• Eigenvalues
  • Resolvent
  • Characteristic polynomial
• Special Matrices
• Schur Complements
  • Domain Decomposition
  • H-Matrices
  • Infinite domains
  • Circuit equivalents
• Resources

Applications

Linear Dynamical Systems

LQR Control

Kalman Filters

Probability

Forbenius Perrod theorem - there is a steady sta probability distribution

Quantum Mechanics

Least Squares Optimization

Boundary Value Problems

Filtering

Fourier transforms Wavelet decompositions PCA

Not sure how to arrange this hierarchy

Matrices

Kronecker products

Numerical

Decompositions

LU

SVD

https://peterbloem.nl/blog/pca-4

Jordan

QR

Eigenvector

Power method

Krylov

Conjugate Gradient

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Eigenvalues

Resolvent

Characteristic polynomial

Special Matrices

List of named matrices

Schur Complements

Domain Decomposition

H-Matrices

Infinite domains

Circuit equivalents

Resources

• Horn, Roger A.; Charles R. Johnson (1985). Matrix Analysis.