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terrytao.wordpress.com | ||
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nickhar.wordpress.com
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| | | | | 1. Low-rank approximation of matrices Let $latex {A}&fg=000000$ be an arbitrary $latex {n \times m}&fg=000000$ matrix. We assume $latex {n \leq m}&fg=000000$. We consider the problem of approximating $latex {A}&fg=000000$ by a low-rank matrix. For example, we could seek to find a rank $latex {s}&fg=000000$ matrix $latex {B}&fg=000000$ minimizing $latex { \lVert A - B... | |
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rjlipton.com
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| | | | | A clever trick on combining automata John Robson, who goes by Mike, has worked on various problems including what is still the best result on separating words-the topic we discussed the other day. Ken first knew him for his proof than $latex {N \times N}&fg=000000$ checkers is $latex {\mathsf{EXPTIME}}&fg=000000$-complete and similar hardness results for chess... | |
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francisbach.com
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| | | | | [AI summary] This technical blog post explores the mathematical properties of symmetric positive definite matrices, specifically focusing on the Löwner order, matrix monotonicity, and matrix convexity in the context of machine learning and optimization. | |
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entangledlogs.com
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| | | To visualize quaternions in the fanciest way, visit Ben eater, Quaternion. Euler angles suffer from a problem of gimbal lock. When rotating around a 3-perpendicular axis in euclidean space, if either two of these axes align i.e becomes parallel, it causes gimbal lock. Once the object is locked, the object will lose one degree of freedom for rotation. This video provides an intuitive explanation of the problem. Pitfalls When converting the Euler angle to a quaternion, it will lose some information. | ||
