AI engineering glossary · Linear algebra
What is spectral norm?
Spectral norm (also called Operator 2-norm): The matrix norm equal to the largest singular value, showing the maximum factor by which the matrix can lengthen any vector. It is used to control how sensitive a layer is to input changes, for example in spectral normalisation.
Spectral norm: an example
A matrix with singular values 5, 2 and 0.3 has spectral norm 5, so no unit vector is stretched beyond length 5.
Related terms
More Linear algebra terms
- Spectral radius
- Spectral theorem
- Standard basis
- Subspace
- Symmetric matrix
- System of linear equations
- Tensor
- Tensor contraction
Where you learn it
Spectral norm is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.