نتایج جستجو برای: linear algebra
تعداد نتایج: 536332 فیلتر نتایج به سال:
For each natural number n, the n-dimensional Euclidean space is denoted by R, and it is a vector space over the real field R (i.e., R is a real vector space). Vectors v1, . . . , vk ∈ R are linearly dependent if there exist c1, . . . , ck ∈ R, not all zero, such that c1v1 + · · ·+ ckvk = 0. If v1, . . . , vk ∈ R are not linearly dependent, then we say they are linearly independent. The span of ...
This note is intended to provide the reader with the necessary linear algebra background to mathematically understand several fundamental topics in machine learning we will be discussing in this course, including (but not limited to) principle component analysis (PCA), singular value decomposition (SVD), and spectral clustering. I am assuming the reader is familiar with Math 54 level concepts f...
We introduce two-dimensional linear algebra, by which we do not mean two-dimensional vector spaces but rather the systematic replacement in linear algebra of sets by categories. This entails the study of categories that are simultaneously categories of algebras for a monad and categories of coalgebras for comonad on a category such as SymMons, the category of small symmetric monoidal categories...
lard, Faster inversion and other black box matrix computations using efficient block
Looking at these five examples where linear algebra comes up in physics, we see that for the first three, involving “classical physics”, we have vectors placed at different points in space and time. On the other hand, the fifth example is a vector space where the vectors are not to be thought of as being simple arrows in the normal, classical space of everyday life. In any case, it is clear tha...
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How can we test the correctness of a computer implementation of an algorithm such as Gaussian elimination, or the QR algorithm for the eigenproblem? This is an important question for program libraries such as LAPACK, that are designed to run on a wide range of systems. We discuss testing based on verifying known backward or forward error properties of the algorithms, with particular reference t...
Development systems for deep learning, such as Theano, Torch, TensorFlow, or MXNet, are easyto-use tools for creating complex neural network models. Since gradient computations are automatically baked in, and execution is mapped to high performance hardware, these models can be trained endto-end on large amounts of data. However, it is currently not easy to implement many basic machine learning...
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