Spectral radius

In mathematics, the spectral radius of a square matrix or a bounded linear operator is the largest absolute value of its eigenvalues (i.e. supremum among the absolute values of the elements in its spectrum). It is sometimes denoted by ρ(·).

Let λ₁, ..., λ_n be the (real or complex) eigenvalues of a matrix A ∈ C^n×n. Then its spectral radius ρ(A) is defined as:

The condition number of ${\displaystyle A}$ can be expressed using the spectral radius as ${\displaystyle \rho (A)\rho (A^{-1})}$.

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