advanced-linear-algebra

Gelfand's formula and when A^n converges to zero

taught

$\lVert A^n\rVert^{1/n}$ converges to $\rho(A)$ as $n\to\infty$, regardless of how badly $\lVert A\rVert$ itself overstated the matrix's growth rate at $n=1$ -- and $A^n\to 0$ exactly when $\rho(A)<1$.

Taught in

Gelfand's formula and when A^n converges to zero
Advanced Linear Algebra

Requires

the-induced-2-norm-and-the-spectral-radius required

Required by

The Neumann series and the resolvent required

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