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nickhar.wordpress.com
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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nhigham.com
The pseudoinverse is an extension of the concept of the inverse of a nonsingular square matrix to singular matrices and rectangular matrices. It is one of many generalized inverses, but the one most useful in practice as it has a number of special properties. The pseudoinverse of a matrix $latex A\in\mathbb{C}^{m\times n}$ is an $latex... |
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www.jeremykun.com
The singular value decomposition (SVD) of a matrix is a fundamental tool in computer science, data analysis, and statistics. It's used for all kinds of applications from regression to prediction, to finding approximate solutions to optimization problems. In this series of two posts we'll motivate, define, compute, and use the singular value decomposition to analyze some data. (Jump to the second post) I want to spend the first post entirely on motivation and background. |
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junglyhh.wordpress.com
Richard Lipton has an article on mathematical disease. My own definition of mathematical disease is quite similar: it must be simple in form, easily explainable to a non-specialist in a few minutes. Moreover, there should be more than one person exclaiming "how can such a problem be open?". Here I also list some problems I... |
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