# Minimizing Vector

• April 1st 2011, 12:42 PM
raed
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.
• April 3rd 2011, 11:15 PM
Drexel28
Quote:

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.
• April 4th 2011, 09:59 AM
raed
Thank you very much for your reply. But what about the vector of minimum norm.
• April 7th 2011, 06:11 PM
mr fantastic
Quote:

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