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Tensor contraction. In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the canonical pairing of a vector space and its dual. In components, it is expressed as a sum of products of scalar components of the tensor (s) caused by applying the summation convention to a pair of dummy indices that are bound to ...
ChatGPT is a chatbot and virtual assistant developed by OpenAI and launched on November 30, 2022. Based on large language models (LLMs), it enables users to refine and steer a conversation towards a desired length, format, style, level of detail, and language. Successive user prompts and replies are considered at each conversation stage as context.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
Twin Cities Public Television, Inc. (abbreviated TPT, doing business as Twin Cities PBS[ 4]) is a nonprofit organization based in Saint Paul, Minnesota, United States, that operates the Twin Cities ' two PBS member television stations, KTCA-TV (channel 2.1) and KTCI-TV (channel 2.3), both licensed to Saint Paul.
The class of 2023 had an average composite score of 19.5, down from 19.8 by the 2022 graduating class. And about 20.8% met all four benchmarks in English, reading, math and science in 2023, down ...
The 1-form ω constructed in this way respects the transitions between overlapping sets, and therefore descends to give a globally defined 1-form on the principal bundle F G E. It can be shown that ω is a principal connection in the sense that it reproduces the generators of the right G action on F G E , and equivariantly intertwines the right ...
e. In mathematics, an algebraic structure consists of a nonempty set A (called the underlying set, carrier set or domain ), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations must satisfy. An algebraic structure may be based on ...
Fidelity’s 2023 Retiree Health Care Cost Estimate found that people who retire at 65 can expect to spend $157,500, on average, for health care and medical expenses throughout their retirement ...