Annihilator of an intersection contains the sum of annihilators
Let $V$ be a vector space and $U$ and $W$ subspaces. Recall that
$$
U^0+W^0 ⊆(U ∩ W)^0 .
$$
When $V$ is an inner product space we have the similar looking inclusion
$$
U^{⟂}+W^{⟂} ⊆(U ∩ W)^{⟂} .
$$
This latter inclusion may be strict outside of finite dimension.
See MSE
So what about the former inclusion?
So what about the former inclusion?
A matrix is normal⇔unitarily diagonalizable
For finite dimensions one has the theorem that a matrix is normal if and only if unitarily diagonalizable.
Strictly upper triangular matrices are nilpotent
Show that every triangular matrix with zeros on the main diagonal is nilpotent.
188 post articles, 21 pages.