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3 exercise(s) shown, 0 hidden
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Find an explicit orthonormal basis for the Hilbert space
[[math]]
H=L^2[0,1]
[[/math]]
by starting with the algebraic basic [math]f_n=x^n[/math] with [math]n\in\mathbb N[/math], and applying Gram-Schmidt.
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
This article was automatically generated from a tex file and may contain conversion errors. If permitted, you may login and edit this article to improve the conversion.
Find all the [math]2\times2[/math] complex matrices
[[math]]
S=\begin{pmatrix}a&b\\ c&d\end{pmatrix}
[[/math]]
which are symmetries, [math]S^2=1[/math], and interpret them geometrically.
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
This article was automatically generated from a tex file and may contain conversion errors. If permitted, you may login and edit this article to improve the conversion.
Prove that any positive operator [math]T\geq0[/math] appears as
[[math]]
T=S^2
[[/math]]
with [math]S[/math] self-adjoint, first in finite dimensions, then in general.