📂Matrix Algebra

Definition of Spectral Radius

Definition

For a matrix $A \in \mathbb{C}^{n \times n}$, the spectral radius is the largest value $\rho (A) = \max \left| \lambda \right|$ among the moduli of its eigenvalues $\lambda_{1} , \cdots , \lambda_{n}$.

Explanation

Generally, the spectrum of a matrix denotes its eigenvalues and eigenvectors collectively; when no matrix is present, the term refers to a corresponding matrix or to eigenvalues and eigenvectors in the abstract linear-algebraic sense¹.

See also

• dominant eigenvalue