1. ## Minimizing Vector

Dear Colleagues:

Show that the subset $\displaystyle M=\{y=(\eta _{j})|\sum \eta _{j}=1 \}$ of complex space $\displaystyle C^{n}$ is complete and convex. Find the vector of minimum norm in $\displaystyle M$.

Regards,

Raed.

2. Originally Posted by raed
Dear Colleagues:

Show that the subset $\displaystyle M=\{y=(\eta _{j})|\sum \eta _{j}=1 \}$ of complex space $\displaystyle C^{n}$ is complete and convex. Find the vector of minimum norm in $\displaystyle M$.

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.