Recent content by gothlev

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...