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pfzhang.wordpress.com | ||
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mikespivey.wordpress.com
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| | | | | The Riemann zeta function $latex \zeta(s)$ can be expressed as $latex \zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s}$, for complex numbers s whose real part is greater than 1. By analytic continuation, $latex \zeta(s)$ can be extended to all complex numbers except where $latex s = 1$. The power sum $latex S_a(M)$ is given by $latex S_a(M) =... | |
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susam.net
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| | | | | [AI summary] The article explains the mathematical properties of fields, demonstrating that a field has only two ideals—{0} and the field itself—and that a commutative ring with only these ideals must be a field. | |
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stephenmalina.com
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| | | | | Selected Exercises # 5.A # 12. Define $ T \in \mathcal L(\mathcal P_4(\mathbf{R})) $ by $$ (Tp)(x) = xp'(x) $$ for all $ x \in \mathbf{R} $. Find all eigenvalues and eigenvectors of $ T $. Observe that, if $ p = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4 $, then $$ x p'(x) = a_1 x + 2 a_2 x^2 + 3 a_3 x^3 + 4 a_4 x^4. | |
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ropmann.wordpress.com
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