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| | Last time, we looked at quarter-tiles. This was an auto-tiling technique for square grids. Each cell in the grid is associated with a terrain (i.e. either solid or empty). Then the squares were spl...
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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...