1. Problem description
Let (e_n)_{n=1}^{\infty} be an orthonormal(ON) basis for H (Hilbert Space). Assume that (f_n)_{n=1}^{\infty} is an ON-sequence in H that satisfies \sum_{n=1}^{\infty} ||e_n-f_n|| < 1 . Show that (f_n)_{n=1}^{\infty} is an ON-basis for H.
Homework Equations...
Thx for the replies. Thank you for a very clear and good explanation (HallsofIvy), the book I am reading is very compact and does not give very good explanations. There was a typo in the end of your reply:
\begin{bmatrix}-21 \\ 13\end{bmatrix}
should be
\begin{bmatrix}-21 \\...
Hi !
I am a little bit confused with notation in the following:
Let A=
\begin{bmatrix}
2 & 3 & 4 \\
8 & 5 & 1 \\
\end{bmatrix}
and consider A as a linear transformation mapping \mathbb{R}^3 to \mathbb{R}^2. Find the matix representation of A with respect to the bases...