AI engineering glossary · Linear algebra
What is spectral radius?
Spectral radius: The largest absolute value among a square matrix's eigenvalues. It tells whether repeatedly applying the matrix makes vectors grow or shrink, so it governs stability of iterations and of recurrent network dynamics.
Spectral radius: an example
A matrix with eigenvalues 0.9 and -0.5 has spectral radius 0.9, so repeated multiplication shrinks vectors towards zero.
Related terms
More Linear algebra terms
- Spectral theorem
- Standard basis
- Subspace
- Symmetric matrix
- System of linear equations
- Tensor
- Tensor contraction
- Tensor rank
Where you learn it
Spectral radius is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.