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:
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!
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).
how do I go from: "a dot product of vector with himself is 0 iff it is 0 itself" to: if the dot product of (which is some vector in ) with each of the basis vectors is 0, then u is 0"?