Hi MHF,

I did badly (failed) in the final exam on linear algebra (4.4/10) and so I must retake the exam in late June or early July. I'm still stuck on some exam questions :

Tell whether this is true or false : Let

and

be vector spaces and

an isomorphism. If

has an inner product

, then

defines an inner product in

.

I admit that I'm totally lost. I don't know what theorem(s) could be useful...

Although

is an isomorfism, I don't think it imples that

and

have the same dimension... I don't even know what are

and

.

Is

the identity linear transformation? If so, I guess it's almost obvious that the answer is "true".