advanced-linear-algebra
Change of basis for forms: congruence, not similarity
taught
A form's matrix transforms as P^T A P under a change of basis -- congruence -- a genuinely different relation from a map's P^{-1}AP similarity.
Taught in
-
Change of basis for forms: congruence, not similarity
Advanced Linear Algebra
Requires
- gram-matrix-of-a-form required
- the-change-of-coordinates-matrix required
Required by
- Sylvester's law of inertia required
Local knowledge map
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.