Lesson 9 of 10Article16 min
SVD & Spectral Theorem Preview
Symmetric real matrices are orthogonally diagonalisable (spectral theorem). For general matrices, the Singular Value Decomposition A = UΣVᵀ always exists and powers compression, PCA, and pseudoinverses.
The workhorse decompositions
Symmetric real matrices are orthogonally diagonalisable (spectral theorem). For general matrices, the Singular Value Decomposition A = UΣVᵀ always exists and powers compression, PCA, and pseudoinverses.
- Low-rank approximation: keep top-k singular values (Eckart–Young).
- Condition number ≈ σ_max / σ_min — sensitivity of solving Ax=b.