advanced-linear-algebra

The induced 2-norm and the spectral radius

taught

$\lVert A\rVert_2$ (the largest singular value) and $\rho(A)$ (the largest $|\lambda|$) both measure a matrix's own "size," but they can genuinely differ for a non-normal matrix -- equal only when A is normal.

Taught in

The induced 2-norm and the spectral radius
Advanced Linear Algebra

Requires

matrix-norms-and-operator-norms required
the-eckart-young-theorem required

Required by

Compact operators: an introductory look required
Gelfand's formula and when A^n converges to zero required

Local knowledge map

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