Help with a proof about inner product space

Hi guys.

I need help with the following:

Let be a vector space over .

Let be a base for .

a. let such that for every : . prove that .

b. let such that for every : . prove that .

this is what I tried so far:

a.

let . since is base for , then:

not sure what's next, though. what am I missing here?

Am I even in the right direction?

Thanks in advanced!

Re: Help with a proof about inner product space

Quote:

Originally Posted by

**Stormey** Let

be a vector space over

.

Let

be a base for

.

a. let

such that for every

:

. prove that

.

b. let

such that for every

:

. prove that

.

For part a):

Recall that .

Now because then

You finish the proof of part a.

Re: Help with a proof about inner product space

Thanks for the help, Plato.

Quote:

Originally Posted by

**Plato** For part a):

Recall that

.

Now because

then

You finish the proof of part a.

how come?

let's say j=2, how do I use this fact here:

Re: Help with a proof about inner product space

Quote:

Originally Posted by

**Stormey** let's say j=2, how do I use this fact here:

Re: Help with a proof about inner product space

Re: Help with a proof about inner product space

Quote:

Originally Posted by

**Stormey** I'm sorry, I guess I'm missing something here.

I'll start over, and use some other letter to clarify my question.

is some vector in vector space

, such that

for every i (

, and

is base).

That changes nothing of what I have posted above.

**is a basis** and the vector has the property that

Using the basis ,

so

Re: Help with a proof about inner product space

Thank you!

now it is clear. :)