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Google Matrix
A Google matrix is a particular stochastic matrix that is used by Google's PageRank algorithm. The matrix represents a graph with edges representing links between pages. The PageRank of each page can then be generated iteratively from the Google matrix using the power method. However, in order for the power method to converge, the matrix must be stochastic, irreducible and aperiodic. Adjacency matrix ''A'' and Markov matrix ''S'' In order to generate the Google matrix ''G'', we must first generate an adjacency matrix ''A'' which represents the relations between pages or nodes. Assuming there are ''N'' pages, we can fill out ''A'' by doing the following: # A matrix element A_ is filled with 1 if node j has a link to node i, and 0 otherwise; this is the adjacency matrix of links. # A related matrix ''S'' corresponding to the transitions in a Markov chain of given network is constructed from ''A'' by dividing the elements of column "j" by a number of k_j=\Sigma_^N A_ where k_j is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Google Search
Google Search (also known simply as Google) is a search engine provided by Google. Handling more than 3.5 billion searches per day, it has a 92% share of the global search engine market. It is also the most-visited website in the world. The order of search results returned by Google is based, in part, on a priority rank system called "PageRank". Google Search also provides many different options for customized searches, using symbols to include, exclude, specify or require certain search behavior, and offers specialized interactive experiences, such as flight status and package tracking, weather forecasts, currency, unit, and time conversions, word definitions, and more. The main purpose of Google Search is to search for text in publicly accessible documents offered by web servers, as opposed to other data, such as images or data contained in databases. It was originally developed in 1996 by Larry Page, Sergey Brin, and Scott Hassan. In 2011, Google introduced "Google Voice ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Web Search Engines
A search engine is a software system designed to carry out web searches. They search the World Wide Web in a systematic way for particular information specified in a textual web search query. The search results are generally presented in a line of results, often referred to as search engine results pages (SERPs). When a user enters a query into a search engine, the engine scans its index of web pages to find those that are relevant to the user's query. The results are then ranked by relevancy and displayed to the user. The information may be a mix of links to web pages, images, videos, infographics, articles, research papers, and other types of files. Some search engines also mine data available in databases or open directories. Unlike web directories and social bookmarking sites, which are maintained by human editors, search engines also maintain real-time information by running an algorithm on a web crawler. Any internet-based content that can't be indexed and searched ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perron–Frobenius Theorem
In matrix theory, the Perron–Frobenius theorem, proved by and , asserts that a real square matrix with positive entries has a unique largest real eigenvalue and that the corresponding eigenvector can be chosen to have strictly positive components, and also asserts a similar statement for certain classes of nonnegative matrices. This theorem has important applications to probability theory (ergodicity of Markov chains); to the theory of dynamical systems ( subshifts of finite type); to economics ( Okishio's theorem, Hawkins–Simon condition); to demography ( Leslie population age distribution model); to social networks ( DeGroot learning process); to Internet search engines (PageRank); and even to ranking of football teams. The first to discuss the ordering of players within tournaments using Perron–Frobenius eigenvectors is Edmund Landau. Statement Let positive and non-negative respectively describe matrices with exclusively positive real numbers as elements and matrices ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transfer Operator
Transfer may refer to: Arts and media * ''Transfer'' (2010 film), a German science-fiction movie directed by Damir Lukacevic and starring Zana Marjanović * ''Transfer'' (1966 film), a short film * ''Transfer'' (journal), in management studies * "The Transfer" (''Smash''), a television episode *''The Transfer'', a novel by Silvano Ceccherini Finance * Transfer payment, a redistribution of income and wealth by means of the government making a payment * Balance transfer, transfer of the balance (either of money or credit) in an account to another account * Money transfer (other) ** Wire transfer, an international expedited bank-to-bank funds transfer Science and technology Learning and psychology * Transfer (propaganda), a method of psychological manipulation * Knowledge transfer, within organizations * Language transfer, in which native-language grammar and pronunciation influence the learning and use of a second language * Transfer of learning, in education Mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Larry Page
Lawrence Edward Page (born March 26, 1973) is an American business magnate, computer scientist and internet entrepreneur. He is best known for co-founding Google with Sergey Brin. Page was the chief executive officer of Google from 1997 until August 2001 (stepping down in favor of Eric Schmidt) then from April 2011 until July 2015 when he moved to become CEO of Alphabet Inc. (created to deliver "major advancements" as Google's parent company), a post he held until December 4, 2019. He remains an Alphabet board member, employee, and controlling shareholder. Creating Google helped Page build a significant amount of wealth. As of November 2022, Page has an estimated net worth of $84 billion according to the Bloomberg Billionaires Index, making him the ninth-richest person in the world. He has also invested in flying car startups Kitty Hawk and Opener. Page is the co-creator and namesake of PageRank, a search ranking algorithm for Google. He received the Marconi Prize in 2004 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sergey Brin
Sergey Mikhailovich Brin (russian: link=no, Сергей Михайлович Брин; born August 21, 1973) is an American business magnate, computer scientist, and internet entrepreneur, who co-founded Google with Larry Page. Brin was the president of Google's parent company, Alphabet Inc., until stepping down from the role on December 3, 2019. He and Page remain at Alphabet as co-founders, controlling shareholders, board members, and employees. As of November 2022, Brin is the 12th-richest person in the world, with an estimated net worth of $78.0 billion. Brin immigrated to the United States with his family from the Soviet Union at the age of six. He earned his bachelor's degree at the University of Maryland, College Park, following in his father's and grandfather's footsteps by studying mathematics, as well as computer science. After graduation, he enrolled in Stanford University to acquire a PhD in computer science. There he met Page, with whom he built a web search e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arnoldi Iteration
In numerical linear algebra, the Arnoldi iteration is an eigenvalue algorithm and an important example of an iterative method. Arnoldi finds an approximation to the eigenvalues and eigenvectors of general (possibly non-Hermitian) matrices by constructing an orthonormal basis of the Krylov subspace, which makes it particularly useful when dealing with large sparse matrices. The Arnoldi method belongs to a class of linear algebra algorithms that give a partial result after a small number of iterations, in contrast to so-called ''direct methods'' which must complete to give any useful results (see for example, Householder transformation). The partial result in this case being the first few vectors of the basis the algorithm is building. When applied to Hermitian matrices it reduces to the Lanczos algorithm. The Arnoldi iteration was invented by W. E. Arnoldi in 1951. Krylov subspaces and the power iteration An intuitive method for finding the largest (in absolute value) eigenvalu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
