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Tensor (other)
A tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensor may also refer to: Mathematics * Tensor (intrinsic definition) * Tensor field * Tensor product * Tensor (obsolete), the norm used on the quaternion algebra in William Rowan Hamilton's work; see * Symmetric tensor, a tensor that is invariant under a permutation of its vector arguments Computer Science * Tensor (machine learning), the application tensors to artificial neural networks * Tensor Processing Unit, an integrated circuit developed by Google for neural network machine learning * Google Tensor, a system on a chip (Soc) found on the Pixel 6 and Pixel 6 Pro smartphones * TensorFlow, a technology developed by Google Other uses * Tensor Trucks, a skateboarding truck company See also * Tensor muscle (other) * Tensor type, in tensor analysis * : Tensors * Glossary of tensor theory * Curvature tensor (other) * St ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors (which are the simplest tensors), dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product. Tensors are defined independent of any basis, although they are often referred to by their components in a basis related to a particular coordinate system. Tensors have become important in physics because they provide a concise mathematical framework for formulating and solving physics problems in areas such as mechanics ( stress, elasticity, fluid mechanics, moment of inertia, ...), electrodynamics ( electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, ...), general relativity (stress–energy tenso ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
TensorFlow
TensorFlow is a free and open-source software library for machine learning and artificial intelligence. It can be used across a range of tasks but has a particular focus on training and inference of deep neural networks. "It is machine learning software being used for various kinds of perceptual and language understanding tasks" – Jeffrey Dean, minute 0:47 / 2:17 from YouTube clip TensorFlow was developed by the Google Brain team for internal Google use in research and production. The initial version was released under the Apache License 2.0 in 2015. Google released the updated version of TensorFlow, named TensorFlow 2.0, in September 2019. TensorFlow can be used in a wide variety of programming languages, including Python, JavaScript, C++, and Java. This flexibility lends itself to a range of applications in many different sectors. History DistBelief Starting in 2011, Google Brain built DistBelief as a proprietary machine learning system based on deep learning neur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curvature Tensor (other)
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In differential geometry, the term curvature tensor may refer to: * the Riemann curvature tensor of a Riemannian manifold — see also Curvature of Riemannian manifolds; * the curvature of an affine connection or covariant derivative (on tensors); * the curvature form of an Ehresmann connection: see Ehresmann connection, connection (principal bundle) or connection (vector bundle). It is one of the numbers that are important in the Einstein field equations. See also *Tensor (other) A tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensor may also refer to: Mathematics * Tensor (intrinsic definition) * Tensor field * Tensor product * Tenso ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glossary Of Tensor Theory
This is a glossary of tensor theory. For expositions of tensor theory from different points of view, see: * Tensor * Tensor (intrinsic definition) * Application of tensor theory in engineering science For some history of the abstract theory see also multilinear algebra. Classical notation ;Ricci calculus :The earliest foundation of tensor theory – tensor index notation. ;Tensor order, Order of a tensor :The components of a tensor with respect to a basis is an indexed array. The ''order'' of a tensor is the number of indices needed. Some texts may refer to the tensor order using the term ''degree'' or ''rank''. ;Tensor rank, Rank of a tensor :The rank of a tensor is the minimum number of rank-one tensor that must be summed to obtain the tensor. A rank-one tensor may be defined as expressible as the outer product of the number of nonzero vectors needed to obtain the correct order. ;Dyadic tensor :A ''dyadic'' tensor is a tensor of order two, and may be represented as a square ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
:Category: Tensors
{{Cat main, Tensor In mathematics, a tensor is a certain kind of geometrical entity and array concept. It generalizes the concepts of scalar, vector and linear operator, in a way that is independent of any chosen frame of reference. For example, doing rotations over axis does not affect at all the properties of tensors, if a transformation law is followed. Tensors are of importance in pure and applied mathematics, physics and engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang .... Multilinear algebra Differential geometry Mathematical physics Engineering concepts ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor Type
In tensor analysis, a mixed tensor is a tensor which is neither strictly covariant nor strictly contravariant; at least one of the indices of a mixed tensor will be a subscript (covariant) and at least one of the indices will be a superscript (contravariant). A mixed tensor of type or valence \binom, also written "type (''M'', ''N'')", with both ''M'' > 0 and ''N'' > 0, is a tensor which has ''M'' contravariant indices and ''N'' covariant indices. Such a tensor can be defined as a linear function which maps an (''M'' + ''N'')-tuple of ''M'' one-forms and ''N'' vectors to a scalar. Changing the tensor type Consider the following octet of related tensors: T_, \ T_ ^\gamma, \ T_\alpha ^\beta _\gamma, \ T_\alpha ^, \ T^\alpha _, \ T^\alpha _\beta ^\gamma, \ T^ _\gamma, \ T^ . The first one is covariant, the last one contravariant, and the remaining ones mixed. Notationally, these tensors differ from each other by the covariance/contravariance of their indices. A given contra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor Muscle (other)
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A tensor muscle has the function of tensing (stretching or tightening) a part and may refer to: * Tensor fasciae latae muscle * Tensor tympani muscle * Tensor vastus intermedius muscle * Tensor veli palatini muscle The tensor veli palatini muscle (tensor palati or tensor muscle of the velum palatinum) is a broad, thin, ribbon-like muscle in the head that tenses the soft palate. Structure The tensor veli palatini is found anterior-lateral to the levator ve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor Trucks
Tensor Trucks is a skateboarding truck company founded and designed by professional skateboarder, Rodney Mullen, in 2000. Tensor's parent company is Dwindle Distribution. The company offers trucks in three different heights (lo, mid, hi) that are tailored for different wheel diameters—the hi is designed for 58mm wheels and smaller; the mid for 54mm or smaller; and the lo for 52mm and smaller. Mullen holds US patent no. 6,443,471B1 for design features implemented in Tensors. Tensor's trucks are manufactured in China. History Mullen explained the origin of the brand in a 2010 interview: I didn’t feel it was legitimate to just build another truck like an Indy ndependent Truck Co. I thought, ‘How can I do it differently?’ The way I skate was flip tricks—setting up your feet and landing ... I wanted to build a truck that would help you do those kind of things better. I wanted to build a truck that doesn’t turn that well because that’s going to help me. If you want ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Google Tensor
Google Tensor is a series of ARM64-based system-on-chip (SoC) processors designed by Google for its Pixel devices. The first-generation chip debuted on the Pixel 6 smartphone series in 2021, and were succeeded by the second-generation chip on the Pixel 7 and Pixel 7 Pro smartphone series in 2022. Background Conceptual development of a Google-designed system-on-chip (SoC) first began in April 2016, although Google CEO Sundar Pichai and hardware chief Rick Osterloh agreed it would likely take an extended period of time before the product was ready; Osterloh stated "about a year in, 2017, we decided we actually really needed to build an SoC, because you couldn't just build a single co-processor in order to really harness the full capabilities we needed across a diverse set of AI models and approaches" and Pichai agreed, adding that " ooglehave also tried to push the boundary with ensor Processing Unitscustom-built for our AI services. I think it's important, recognizing that t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor (intrinsic Definition)
In mathematics, the modern component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multilinear concept. Their properties can be derived from their definitions, as linear maps or more generally; and the rules for manipulations of tensors arise as an extension of linear algebra to multilinear algebra. In differential geometry an intrinsic geometric statement may be described by a tensor field on a manifold, and then doesn't need to make reference to coordinates at all. The same is true in general relativity, of tensor fields describing a physical property. The component-free approach is also used extensively in abstract algebra and homological algebra, where tensors arise naturally. :''Note: This article assumes an understanding of the tensor product of vector spaces without chosen bases. An overview of the subject can be found in the main tensor article.'' Definition via tensor products of vector spaces Given ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor Processing Unit
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. 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 offering a smaller version of the chip for sale. Overview The tensor processing unit was announced in May 2016 at Google I/O, when the company said that the TPU had already been used inside their data centers for over a year. The chip has been specifically designed for Google's TensorFlow framework, a symbolic math library which is used for machine learning applications such as neural networks."TensorFlow: Open source machine learning" "It is machine learning software being use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Neural Networks
Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains. An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons. An artificial neuron receives signals then processes them and can signal neurons connected to it. The "signal" at a connection is a real number, and the output of each neuron is computed by some non-linear function of the sum of its inputs. The connections are called ''edges''. Neurons and edges typically have a '' weight'' that adjusts as learning proceeds. The weight increases or decreases the strength of the signal at a connection. Neurons may have a threshold such that a signal is sent only if the aggregate signal crosses that threshold. Typicall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
