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All time greatest eigenvectors | Raymond’s Weblog^

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Formally, for a given linear transformation, its eigenvectors are the vectors that get scaled up by a constant. A linear transformation is a way of mapping all the points in a space so that, if some points form a straight line in the original space, they’ll be mapped to points that also form a line, and the point in the centre doesn’t move. In 2 dimensions, the only linear transformations are combinations of stretching and rotating things. The eigenvectors here are basically the lines which start from the centre and are just stretched or squeezed by the transformation. So in fact, they’re effectively also the lines along which you’re doing the stretching. There’s a good introduction here by 3Blue1Brown which covers the maths. But this post isn’t an introduction to what eigenvectors are. It’s about what they’re for, why they might be interesting, and why someone (like me) would actually find them aesthetically appealing or, dare I say it, beautiful. I love all rotational axes, but this

All time greatest eigenvectors | Raymond’s Weblog^ Raymond's Weblog^ All time greatest eigenvectors Brief intro to eigenvectors Formally, for a given linear transformation, its eigenvectors are the vectors that get scaled up by a constant. A linear transformation is a way of mapping all the points in a space so that, if some points form a straight line in the original space, they’ll be mapped to points that also form a line, and the point in the centre doesn’t move. In 2 dimensions, the only linear transformations are combinations of stretching and rotating things. The eigenvectors here are ba

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