Every self-adjoint (Hermitian) operator on a finite-dim inner-product space is unitarily diagonalizable with real eigenvalues. Cornerstone of quantum mechanics (observables) and PCA.
Spectral theorem
Related concepts
- Eigenvalue / eigenvector
- Inner product
- Singular value decomposition (SVD)
- Positive-definite matrix
- Separation of variables
- Schur decomposition
- Polar decomposition
- Schrödinger equation
- Energy quantization
- Hilbert space (physics use)
- Sturm–Liouville theory (physics use)
- Tidal / Jacobi stability eigenstructure (astrophysical N-body)
- Hartree-Fock theory
- Electron correlation