Math Is Fun Forum

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Linear algebra

Let

be a subspace of

and its orthogonal complement respectively

defined projection operator

. And

has the property

Then my book says, the range of

is

, this is obvious

but I never get how it could conclude that  the null space of

is

I try assuming , 

and can't reach any contradiction.

thanks in advance.

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Re: Linear algebra

Ah, nvm, it follows right from the orthogonal decomposition of a vector.