⧼exchistory⧽
6 exercise(s) shown, 0 hidden
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Prove the following formula, with [math]w=e^{2\pi i/N}[/math],
[[math]]
\frac{1}{N}\sum_kw^{jk}=\delta_{0j}
[[/math]]
where all the indices, and the Kronecker symbol too, are taken modulo [math]N[/math].
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.
Compute the determinant of the Fourier matrix [math]F_N[/math].
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.
Diagonalize the Fourier matrix [math]F_N[/math].
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 the deformed Fourier matrices [math]F_4^s[/math] are not equivalent to each other, up to identifying [math]\{s,-s,\bar{s},-\bar{s}\}[/math].
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 a simple formula for the Tao matrix [math]T_6[/math].
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 the Beauchamp-Nicoara matrix [math]BN_6^q[/math] is indeed Hadamard.