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CuPy is an open source library for GPU-accelerated computing with Python programming language, providing support for multi-dimensional arrays, sparse matrices, and a variety of numerical algorithms implemented on top of them. [3]
Pandas (styled as pandas) is a software library written for the Python programming language for data manipulation and analysis. In particular, it offers data structures and operations for manipulating numerical tables and time series .
Tensor Processing Unit (TPU) is an AI accelerator application-specific integrated circuit (ASIC) developed by Google for neural network machine learning, using Google's own TensorFlow software. [2] Google began using TPUs internally in 2015, and in 2018 made them available for third-party use, both as part of its cloud infrastructure and by ...
In mathematics and physics, a tensor field is a function assigning a tensor to each point of a region of a mathematical space (typically a Euclidean space or manifold) or of the physical space. Tensor fields are used in differential geometry , algebraic geometry , general relativity , in the analysis of stress and strain in material object, and ...
The tensor product of two vector spaces is a vector space that is defined up to an isomorphism.There are several equivalent ways to define it. Most consist of defining explicitly a vector space that is called a tensor product, and, generally, the equivalence proof results almost immediately from the basic properties of the vector spaces that are so defined.
A rank-tensor is called a border tensor if there exists a sequence of tensors of rank at most < whose limit is . If r {\displaystyle r} is the least value for which such a convergent sequence exists, then it is called the border rank of A {\displaystyle {\mathcal {A}}} .
A plot located on the intersection of row and j th column is a plot of variables X i versus X j. [10] This means that each row and column is one dimension, and each cell plots a scatter plot of two dimensions. [citation needed] A generalized scatter plot matrix [11] offers a range of displays of paired combinations of categorical and ...
Clearly this pseudotensor for gravitational stress–energy is constructed exclusively from the metric tensor and its first derivatives. Consequently, it vanishes at any event when the coordinate system is chosen to make the first derivatives of the metric vanish because each term in the pseudotensor is quadratic in the first derivatives of the ...