Let be a fixed real number and let and .
Given a vector in , write it as a linear combination .
It also asked me to prove that was an orthonormal basis for so I did that.
However,
. and
Can someone assist me on where to go from here? Thank you!
Let be a fixed real number and let and .
Given a vector in , write it as a linear combination .
It also asked me to prove that was an orthonormal basis for so I did that.
However,
. and
Can someone assist me on where to go from here? Thank you!
Hello,
I'm not sure what you're trying to get ?
Did you prove that it was an orthonormal basis ?
If you're looking for and , then... :
Because the scalar product is bilinear, this is equal to :
But . Here, because it's an orthonormal basis.
And because it's an orthonormal basis.
Therefore,
If you prefer, the scalar product of y with the n-th vector of an orthonormal basis represents the n-th coordinate of y in this basis. (this is extra info and I'm not sure I explained it well )