Spectral Radius (eigenstuff)¶
Definition¶
The maximum modulus of the eigenvalues, \(\text{max}\{|\lambda| \ : \ \lambda \in \lambda(\mathbf{A}) \}\), is called the spectral radius of \(\mathbf{A}\), denoted \(\rho(\mathbf{A})\).
"Maximum modulus of the eigenvalues" just means the eigenvalue with the largest absolute value.
Intuitively, the spectral radius tells you how much the matrix can stretch a vector in any direction during repeated application \(\mathbf{A}^k\).