advanced-linear-algebra
Cyclic subspaces and companion matrices
taught
A single vector v, repeatedly hit with T, can span an entire invariant subspace -- and relative to that spanning chain, T's matrix is a companion matrix built entirely from one polynomial's coefficients.
Taught in
-
Cyclic subspaces and companion matrices
Advanced Linear Algebra
Requires
- the-minimal-polynomial required
Required by
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.