# Math Help - Minimizing Vector

1. ## Minimizing Vector

Dear Colleagues:

Could you please help me in solving the following problem:
Show that the subset $M=\{y=(\eta _{j})|\sum \eta _{j}=1 \}$ of complex space $C^{n}$ is complete and convex. Find the vector of minimum norm in $M$.

Regards,

Raed.

2. Originally Posted by raed
Dear Colleagues:

Could you please help me in solving the following problem:
Show that the subset $M=\{y=(\eta _{j})|\sum \eta _{j}=1 \}$ of complex space $C^{n}$ is complete and convex. Find the vector of minimum norm in $M$.

Regards,

Raed.
It's complete because it's clearly closed and closed subspaces of complete spaces are complete...for convexity I think you may be thinking too hard.

3. Thank you very much for your reply. But what about the vector of minimum norm.

4. Originally Posted by raed
Thank you very much for your reply. But what about the vector of minimum norm.