AI engineering glossary · Linear algebra
What is spectral theorem?
Spectral theorem: A result stating that a real symmetric matrix can be written using orthogonal eigenvectors and real eigenvalues. It guarantees clean, stable eigen-analysis for covariance and Gram matrices, which is why those matrices behave so well in machine learning.
Spectral theorem: an example
Any covariance matrix of features can be written as Q D Q^T with orthogonal Q and non-negative diagonal D.
Related terms
More Linear algebra terms
- Standard basis
- Subspace
- Symmetric matrix
- System of linear equations
- Tensor
- Tensor contraction
- Tensor rank
- Trace
Where you learn it
Spectral theorem is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.