- #1
Bipolarity
- 776
- 2
Suppose ##A## is a ## n \times n## matrix.
Define the set ## V = \{ B | AB = BA, B \in M_{n \times n}( \mathbb{F}) \} ##
I know that ##V## is a subspace of ##M_{n \times n}( \mathbb{F}) ## but how might I go about finding the dimension of ##V##? Is this even possible? It seems like an interesting problem, but constructing a basis for ##V## seems to me challenging enough. Any tips for me?
Thanks!
P.S. Not a homework problem, I made it myself and not sure if it has a simple answer.
BiP
Define the set ## V = \{ B | AB = BA, B \in M_{n \times n}( \mathbb{F}) \} ##
I know that ##V## is a subspace of ##M_{n \times n}( \mathbb{F}) ## but how might I go about finding the dimension of ##V##? Is this even possible? It seems like an interesting problem, but constructing a basis for ##V## seems to me challenging enough. Any tips for me?
Thanks!
P.S. Not a homework problem, I made it myself and not sure if it has a simple answer.
BiP