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nickhar.wordpress.com | ||
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www.ethanepperly.com
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fabricebaudoin.blog
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| | | | | In this section, we consider a diffusion operator $latex L=\sum_{i,j=1}^n \sigma_{ij} (x) \frac{\partial^2}{ \partial x_i \partial x_j} +\sum_{i=1}^n b_i (x)\frac{\partial}{\partial x_i}, $ where $latex b_i$ and $latex \sigma_{ij}$ are continuous functions on $latex \mathbb{R}^n$ and for every $latex x \in \mathbb{R}^n$, the matrix $latex (\sigma_{ij}(x))_{1\le i,j\le n}$ is a symmetric and non negative matrix. Our... | |
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theoryofcomputing.org
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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): | ||
