Page 219 - Linear Algebra Done Right
P. 219
The Characteristic Polynomial
This equation, along with 9.23, shows that dim V = dim U. Because U
is a subspace of V, this implies that V = U. In other words,
V = U 1 +· · ·+ U m + V 1 + ··· + V M . 209
This equation, along with 9.23, allows us to use 2.19 to conclude that
(a) holds, completing the proof.
