dominant eigenvalue

Whichever eigenvalue of a matrix has the largest absolute value -- the one that ends up controlling A^k v for large k.

An eigenvalue $\lambda_1$ of $A$ is dominant (or strictly dominant) if $\lvert\lambda_1\rvert>\lvert\lambda_i\rvert$ for every other eigenvalue $\lambda_i$ of $A$ . When a strictly dominant eigenvalue exists, repeatedly applying $A$ to almost any starting vector amplifies its $\lambda_1$ -component fastest, which is exactly the mechanism the power method exploits.

Examples

Eigenvalues $5, -3, 2$ : $5$ is strictly dominant. Eigenvalues $5, -5, 2$ : NEITHER is dominant, since the two largest tie in magnitude.