- #1
mnb96
- 715
- 5
Hello,
I have a (infinite dimensional) vector space and defined an inner product on it.
The vectors element are infinite sequence of real numbers [tex](x_1, x_2,\ldots)[/tex].
The inner product has the common form: [tex]x_iy_i[/tex]
The problem now is that the vectors have an infinite number of elements, so the L2-norm of many vectors would be eventually equal to +Infinity.
- Is that admitted?
- How can one define an orthonormal base for such a space?
I have a (infinite dimensional) vector space and defined an inner product on it.
The vectors element are infinite sequence of real numbers [tex](x_1, x_2,\ldots)[/tex].
The inner product has the common form: [tex]x_iy_i[/tex]
The problem now is that the vectors have an infinite number of elements, so the L2-norm of many vectors would be eventually equal to +Infinity.
- Is that admitted?
- How can one define an orthonormal base for such a space?