Hello

Let be our set.

The sum and the scalar product are defined normally.

How can i prove that this set is with those operations is isomorphic to ?

Thanks

Printable View

- October 24th 2010, 05:29 PMosodudVector space isomorphic to R^n+1
Hello

Let be our set.

The sum and the scalar product are defined normally.

How can i prove that this set is with those operations is isomorphic to ?

Thanks - October 24th 2010, 06:08 PMTheEmptySet
- October 25th 2010, 05:16 AMHallsofIvy
A very general and not very difficult theorem- if two finite dimensional vector spaces have the same dimension, then they are isomorphic.

That is, if U has dimension n, then it has a basis . If V also has dimension n, then it has a basis . The function, , defined by and extended "by linearity" is an isomorphism.