📂Matrix Algebra

Definition of Spectral Radius

Definition

The eigenvalue $\lambda_{1} , \cdots , \lambda_{n}$ of the matrix $A \in \mathbb{C}^{n \times n}$ with the largest modulus $\rho (A) = \argmax_{\lambda} \left| \lambda \right|$ is called the Spectral Radius.

Explanation

Usually, the spectra of a matrix refers to both its eigenvalues and eigenvectors collectively, and in the absence of a matrix, it denotes the matrix or the abstractly defined eigenvalues and eigenvectors algebraically¹.