Consider the matrix [tex]A = u v^{\ast }[/tex] where [tex]u, v \in \textbf{C}^{n}[/tex]. Under what condition on u and v is A a projector?(adsbygoogle = window.adsbygoogle || []).push({});

A is a projector if [tex]A^{2}=A [/tex], so we have [tex]u v^{*} u v^{*}= u v^{\ast }[/tex].

Does this imply [tex] u v^{\ast } = I[/tex] ? And what exactly are the conditions on u and v that they are asking?

do we have that [tex]u_{i} v^{\ast }_{i}=1[/tex] and [tex]u_{i} v^{\ast }_{j}=0[/tex] for [tex] i\neq j[/tex] ?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Projector matrices

**Physics Forums | Science Articles, Homework Help, Discussion**