advanced-linear-algebra

The Neumann series and the resolvent

taught

$(I-A)^{-1}=I+A+A^2+\cdots$ converges exactly when $\rho(A)<1$, the identical condition Gelfand's formula names -- the matrix generalization of the geometric series.

Taught in

The Neumann series and the resolvent
Advanced Linear Algebra

Requires

gelfands-formula-and-when-a-n-converges-to-zero required

Required by

Conditioning and the perturbation of eigenvalues required

Local knowledge map

Click to expand

Solid arrows are required prerequisites; dashed are recommended or helpful. Lower rows are more foundational. Click any box to jump to that concept.