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www.sirver.net | ||
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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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nulliq.dev
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| | | | | In search of a better dot product | |
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arkadiusz-jadczyk.eu
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| | | | | We continue Becoming anti de Sitter. Every matrix $\Xi$ in the Lie algebra o(2,2) generates one-parameter group $e^{\Xi t}$ of linear transformations of $\mathbf{R}^4.$ Vectors tangent to orbits of this group form a vector field. Let us find the formula for the vector field generated by $\Xi. | |
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www.scientificamerican.com
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| | | At an American Mathematical Society meeting, high school students presented a proof of the Pythagorean theorem that used trigonometry-an approach that some once considered impossible | ||
