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jasonmaa.com | ||
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www.paepper.com
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| | | | | As a data scientist, you are dealing a lot with linear algebra and in particular the multiplication of matrices. Important properties of a matrix are its eigenvalues and corresponding eigenvectors. So let's explore those a bit to get a better intuition of what they tell you about the transformation. We will just need numpy and a plotting library and create a set of points that make up a rectangle (5 points, so they are visually connected in the plot): | |
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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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eccc.hpi-web.de
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| | | Homepage of the Electronic Colloquium on Computational Complexity located at the Weizmann Institute of Science, Israel | ||
