the-french-artist/wikipedia_20220301.simple_sentence_embeddings huggingface dataset:
Dot product 
 Provided that the basis is orthonormal, the dot product is invariant under isometric changes of the basis: rotations, reflections, and combinations, keeping the origin fixed.
Dot product 
 In other words, for an orthonormal space with any number of dimensions, the dot product is invariant under a coordinate transformation based on an orthogonal matrix.
Dot product 
 The new base vectors have the same length as the old ones (that is, unit length in terms of the old basis).
Dot product 
 This is a very useful identity (also known as Lagrange's formula) involving the dot- and  cross-products.
Dot product 
 so we conclude that taking the dot product of a vector v with itself yields the squared length of the vector.
Dot product 
 Due to the geometric interpretation of the dot product, the norm ||a|| of a vector a in such an inner product space is defined as
Dot product 
 For vectors with complex entries, using the given definition of the dot product would lead to quite different geometric properties.
Dot product 
 For instance, the dot product of a vector with itself can be an arbitrary complex number, and can be zero without the vector being the zero vector; this in turn would have severe consequences for notions like length and angle.
Dot product 
 Many geometric properties can be salvaged, at the cost of giving up the symmetric and bilinear properties of the scalar product, by alternatively defining
Dot product 
 Then the scalar product of any vector with itself is a non-negative real number, and it is nonzero except for the zero vector.
Dot product 
 However, this scalar product is not linear in b (but rather conjugate linear), and the scalar product is not symmetric either, since
Dot product 
 This type of scalar product is nevertheless quite useful, and leads to the notions of Hermitian form and of general inner product spaces.
Dot product 
 It is defined as the sum of the products of the corresponding components of two matrices having the same size.
Dot product 
 If  and  are two tensors with element representation  and  the elements of the dot product  are given by
Dot product 
 This definition naturally reduces to the standard vector dot product when applied to vectors, and matrix multiplication when applied to matrices.
Zapatista Army of National Liberation 
 The Zapatista Army of National Liberation (EZLN; ) is a political and militant group based in –Chiapas, the southernmost state of Mexico.
Zapatista Army of National Liberation 
 Though the movement has many leaders, both women and men, Marcos has become the unofficial spokesperson for the movement.
Zapatista Army of National Liberation 
 This is because he is very well educated, a good public speaker, and has written letters to and worked with writers and intellectuals from all over the world.
Zapatista Army of National Liberation 
 He signs almost all of his letters with "Subcomandante Marcos, from the mountains of the southeast of Mexico."
Zapatista Army of National Liberation 
 He is wearing a ski-mask in every picture and video of him and ski-masks have become a symbol of the EZLN in Mexico, as the majority of its supporters also wear them.
Zapatista Army of National Liberation 
 Followers of the EZLN also paint murals of Marcos in his mask and Emiliano Zapata to show their support.
Zapatista Army of National Liberation 
 The Zapatistas created a 'Council of Good Government' which is a direct democracy representing between 120,000 to 300,000 people.
Zapatista Army of National Liberation 
 The economy is made up of a coordinated network of communal stores, worker cooperatives and family farms.
Zapatista Army of National Liberation 
 The Zapatistas mainly produce corn, beans, coffee, bananas, sugar, cattle, chicken, pigs and clothing.
Lead glass 
 Normal glass has calcium oxide in it, while lead glass changes the calcium oxide with lead(II) oxide.
Lead glass 
 Lead glass has a chemical composition of silicon and lead oxides, with other elements added to get colours or properties.
Lead glass 
 Lead glass is also known as X-ray glass or radiation shielding glass as one of its major applications is in the absorbance of high energy radiation while maintaining optical transparency.
Lead glass 
 The presence and quantity of PbO are what determines some of lead glass’ most important optical and physical properties.
Lead glass 
 In the medical and research fields where visibility is required during procedures or experiments that involve radiation, lead glass can achieve the same radiation attenuation as the surrounding walls or barriers while allowing visibility to the operator.
Lead glass 
 A typical example is the viewing window of an X-ray room or a laboratory experimenting with radioactive materials.
Lead glass 
 The high refractive index of lead glass is useful for the production of lenses as thinner lenses can be crafted to achieve similar focal lengths to ordinary ophthalmic glass.
Lead glass 
 Digital projectors use lead glass because it has a high level of transmission over short wavelengths, which is typical of projector laser beams.
Lead glass 
 Further, the temperature rise caused by the light source does not distort the image projected by lead glass because it has a lower thermal conductivity than lead-free glass.
Lead glass 
 It is useful in instruments that operate in the near-ultraviolet region and the near-infrared region as in bio-fluorescence, gene analyses, spectrometry and telecommunication.
Relic 
 A relic is an object, especially a piece of the body or a personal item of someone of religious importance, that was carefully preserved with an air of veneration as a memorial that you can touch.
Relic 
 Relics are an important aspect of Buddhism, some denominations of Christianity, Hinduism, shamanism, and many other personal belief systems.
Relic 
 Some well-known religious relics include the Tooth of Buddha, the Holy Grail, the Crown of Thorns, the True Cross of Jesus, the Staff of Moses, and the Sword of Mohammed.
John F. Kennedy Jr. 
 John Fitzgerald Kennedy Jr. (November 25, 1960 – July 16, 1999) often called John-John, JFK Jr. or Jack Kennedy Jr. was an American lawyer and magazine publisher.
John F. Kennedy Jr. 
 Kennedy was born at Medstar Georgetown University Hospital in Washington, DC, to President elect John F. Kennedy and his wife Jacqueline.
John F. Kennedy Jr. 
 He spent his first three years at the White House until his father's assassination on November 22, 1963.
Ferdinand Maria, Elector of Bavaria 
 Ferdinand Maria, Elector of Bavaria (31 October 1636 – 26 May 1679) was a Wittelsbach ruler of Bavaria and an elector (Kurfürst) of the Holy Roman Empire from 1651 to 1679.
Ferdinand Maria, Elector of Bavaria 
 He was born in Munich and was the eldest son of Maximilian I, Elector of Bavaria and Maria Anna of Austria a daughter of Ferdinand II, Holy Roman Emperor.
Ferdinand Maria, Elector of Bavaria 
 On 8 December 1650 he married Henriette Adelaide of Savoy, daughter of Victor Amadeus I of Savoy and Christine Marie of France.
Ferdinand Maria, Elector of Bavaria 
 Still a minor he succeeded his father in 1651, his mother and his uncle Albert VI of Bavaria served as regents of Bavaria for three years.
Ferdinand Maria, Elector of Bavaria 
 Ferdinand Maria supported the wars of the Habsburgs against the Ottoman Empire with Bavarian forces (1662-1664).
Ferdinand Maria, Elector of Bavaria 
 The marriage of his eldest daughter Maria Anna and her cousin Louis, Grand Dauphin in 1680 cemented the alliance with France.
Ferdinand Maria, Elector of Bavaria 
 Maria Anna Victoria of Bavaria (28 November 1660 – 20 April 1690) married Louis, Grand Dauphin and had issue; King Juan Carlos I of Spain descends from her.
Ferdinand Maria, Elector of Bavaria 
 Maximilian II Emanuel, Elector of Bavaria (11 July 1662 – 26 February 1726), next Elector of Bavaria; married Maria Antonia of Austria and had issue; married Theresa Kunegunda Sobieska and had issue.
Ferdinand Maria, Elector of Bavaria 
 Violante Beatrice of Bavaria (3 April 1673 – 3 June 1731) married Ferdinando de' Medici, Grand Prince of Tuscany.
Christian apologetics 
 Christian apologetics is a field of Christian theology that tries to find a rational basis for the Christian faith.
Christian apologetics 
 There have been many people who tried to do this, including Paul of Tarsus, Origen, Augustine of Hippo and C. S. Lewis.
Denny Hamlin 
 In 2004, while racing full-time in Late Model Stock Cars, Hamlin was signed to a development program  with Joe Gibbs Racing.
Denny Hamlin 
 He ran his first  ARCA RE/MAX Series race at Talladega Superspeedway, finishing third in the #10 Pontiac owned by Andy Hillenburg.
Denny Hamlin 
 He started twenty-seventh but finished eighth in the #18 Joe Gibbs Driven Performance Oil Chevrolet.
Denny Hamlin 
 Hamlin also raced in his first Nextel Cup Series races in 2005, making his Cup first start at Kansas Speedway as driver of the #11 FedEx Chevrolet.
Denny Hamlin 
 He finished the Sprint Cup season with three top 10 finishes in seven starts and one pole at Phoenix International Raceway.
Denny Hamlin 
 In the Nextel Cup Series, Hamlin won the Raybestos Rookie of the Year award and finished third in the final standings.
Denny Hamlin 
 In the Nationwide Series, Hamlin won three races, Darlington, Michigan, and Dover in the #20 Rockwell Automation Chevy.
Denny Hamlin 
 In 2008, Hamlin finished 8th in the Sprint Cup Series and won early in the season at Martinsville Speedway.
Denny Hamlin 
 He won three races in the Nationwide Series, driving both the #18 and #20 cars for Joe Gibbs Racing, as well as the #32 Dollar General/Haas Avocados car for Braun Racing.
Denny Hamlin 
 It was an emotional win for Hamlin as his grandmother, Thelma Clark, died the Friday before the race.
Denny Hamlin 
 Hamlin also won races at Martinsville Speedway, his home track Richmond International Raceway, and the last race of the year at Homestead-Miami Speedway.
Denny Hamlin 
 On January 22, 2010, Denny Hamlin tore the anterior cruciate ligament in his left knee while playing basketball.
Denny Hamlin 
 This race moved Hamlin into 10th place in the Sprint Cup Series points, and made sure he would have a place in the championship race.
Denny Hamlin 
 Denny Hamlin won 8 races in the 2010 Sprint Cup Series but finished the season 2nd in Sprint Cup Series points behind Jimmie Johnson.
Denny Hamlin 
 Hamlin had mechanical problems many times in 2011, and this hurt his chances at finishing well in the points.
Post-transition metal 
 The post-transition metals, also known as the poor metals, is a group of metals on the periodic table.
Lead(II) bromide 
 It can be made by reacting lead(II) nitrate or lead(II) acetate with hydrobromic acid or any other bromide.
Anderson Cooper 
 Cooper's great-great-great-grandfather was Cornelius Vanderbilt, a 19th-century American businessman and slave owner.
Contra 
 The player plays as Bill Rizer (player 1) or Lance Bean (player 2), as they try to stop and evil extraterrestrial terrorist organization Red Falcon from taking over the planet Earth and making the human species extinct.
Ryan Caldwell 
 He has also played for the New York Islanders and Phoenix Coyotes of the National Hockey League (NHL), the DEG Metro Stars, Eisbären Berlin, and Thomas Sabo Ice Tigers of the DEL, and Ässät and Lukko of the SM-liiga.
Ryan Caldwell 
 As an amateur he was an All-American defenceman and captained the University of Denver Pioneers to the 2004 NCAA Championship.
Aaron MacKenzie 
 Aaron G. MacKenzie (born March 7, 1981, in Terrace Bay, Ontario) is a Canadian former professional ice hockey defenceman.
Connie Madigan 
 Cornelius Dennis "Mad Dog" Madigan (born October 4, 1934, in Port Arthur, Ontario) is a Canadian retired professional ice hockey defenceman notable for being the oldest rookie in National Hockey League history.
Connie Madigan 
 After playing several years in senior leagues in Ontario and British Columbia in the late 1950s, Madigan had a long career as a minor league star, most notably with the Fort Wayne Komets of the International Hockey League for three seasons in the early 1960s, and then for the Portland Buckaroos of the Western Hockey League for nine seasons.
Connie Madigan 
 He won accolades as First Team league All-Star in 1960, 1966, 1967, 1968 and 1969, Second Team All-Star in 1965, 1971 and 1972, as well as winning best defenceman honors in 1966.
Connie Madigan 
 In the 1972–73 NHL season, the St. Louis Blues of the NHL bought Madigan's rights from the Buckaroos, and he joined the Blues in January 1973 at the age of 38, becoming the oldest rookie ever.
Connie Madigan 
 He played for the Blues in twenty regular-season games and five playoff games, before finishing his career with Portland in parts of the two successive seasons.
Connie Madigan 
 At the time of his retirement, Madigan was second in minor league history in career penalty minutes, and is still 62nd in that category.
Connie Madigan 
 In addition to Madigan's hockey career, he had a minor role in the 1977 cult classic movie Slap Shot as legendary hockey goon Ross "Mad Dog" Madison.
JaVale McGee 
 JaVale McGee (born January 19, 1988 in Flint, Michigan) is an American basketball player that currently plays for the Los Angeles Lakers of the National Basketball Association (NBA).
JaVale McGee 
 McGee was drafted by the Washington Wizards with the 18th overall pick in the 1st round of the 2008 NBA Draft.
JaVale McGee 
 McGee also participated in the 2011 NBA Slam Dunk Contest where he finished in second place, losing to Blake Griffin.
JaVale McGee 
 McGee's father was George Montgomery who was also a NBA player and his mother is Pamela McGee who was a WNBA player which made McGee the first son of an WNBA player to play in the NBA.
Kevin Love 
 Kevin Wesley Love (born September 7, 1988 in Santa Monica, California) is an American basketball player that currently plays for the Cleveland Cavaliers of the National Basketball Association (NBA).
Kevin Love 
 He is the son of former NBA player Stan Love and the nephew of founding Beach Boys member Mike Love.
Western grey kangaroo 
 After it comes out of the pouch, it will continue to drink milk from the mother's pouch for about another nine months.
Western grey kangaroo 
 Long known to the Aboriginal people of Australia, for Europeans, the western grey was the centre of a great deal of sometimes comical taxonomic confusion for almost 200 years.
Western grey kangaroo 
 It was first noted by European settlers when the great explorer Matthew Flinders landed on Kangaroo Island in 1802.
Western grey kangaroo 
 In 1803 French explorers captured several Kangaroo Island Western Greys and shipped them home to Paris, where they lived in the zoological gardens for some years.
Western grey kangaroo 
 Eventually, researchers at the Paris Museum of Natural History recognised that these animals were indeed different and formally described the species as Macropus fuliginosus in 1817.
Western grey kangaroo 
 There the matter rested for over 100 years, and it was not until 1917 that researchers realised that the "forester kangaroo" of Tasmania was in fact Macropus giganteus, the same western grey kangaroo that was, and still is, widespread in the more fertile south-eastern part of the mainland.
Western grey kangaroo 
 By 1971, it was understood that the Kangaroo Island species was the same as the kangaroos of southern Western Australia, and that this population extended through much of the eastern part of the continent as well.
Western grey kangaroo 
 There are two subspecies of the western grey: Macropus fuliginosus fuliginosus which lives on Kangaroo Island, and Macropus fuliginosus melanops, which has a range of different types that change gradually from west to east.
Western grey kangaroo 
 The eastern grey does not live over the NSW-South Australia border, but the two species are both common in the Murray-Darling Basin area.
Western grey kangaroo 
 They never interbreed in the wild, although hybrids between eastern grey females and western grey males have been produced in captivity.
Western grey kangaroo 
 The western grey kangaroo is also called the black-faced kangaroo, mallee kangaroo, sooty kangaroo and carno kangaroo.
Traditional animation 
 To make things cheaper, though, people made limited animation that used two to three copies of the same image (so the stop-motion process would be two to three times faster.)
Traditional animation 
 A sketchpad at first may contain a comic book that looks like an animation when the editors flip it back and forth.
Milarepa 
 A collection of his teachings in the form of poetic songs called The Hundred Thousand songs of Milarepa, and his biography The Life of Milarepa are two of the most popular books in Tibet.
Milarepa 
 Together these three (Marpa, Milarepa and Gampopa) are considered to be the founders of the Kagyu school of Tibetan Buddhism.
Milarepa 
 Milarepa was born in the village of Kya Ngatsa in the Gungthang province of western Tibet to a family of farmers.
Milarepa 
 When his father died, Milarepa's uncle and aunt took all of the family's wealth and property and mistreated Milarepa, his mother and sister.
Milarepa 
 At his mother's urging, Milarepa left home and studied magic so that he could take revenge on his uncle and aunt.
Milarepa 
 While his aunt and uncle were having a party to celebrate the marriage of their son, Mila took his revenge by summoning a great hail storm to demolish their house, which killed 35 people.
Milarepa 
 The villagers were angry and set off to look for Milarepa, but his mother got word to him and he sent anther hailstorm to destroy their crops.
Milarepa 
 Mila later came to regret his evil actions and so became determined to practice the Buddha's teachings.
Milarepa 
 Before Marpa would teach Mila, he had him build and then demolish three towers in turn and go through many other trials.
Milarepa 
 After practicing these teacings very diligently for twelve years in remote Himalayan caves of Tibet and Nepal, Mila attained the complete enlightenment.
Milarepa 
 During his meditation practice he ate mostly nettle soup which made his skin turn green, and wore only a single cotton robe.
Milarepa 
 Later Milarepa become a wandering teacher and attracted many disciples, of whom the most well known were Rechungpa and Gampopa.
Milarepa 
 Rechungpa followed the yogic lifestyle of his teacher while Gampopa, a Kadampa monk, eventually established a monastery a Daglha Gampo which became the first Kagyu institution.
Milarepa 
 Later Gampopa's immediate disciples and their successors established the various branches of the Kagyu school of Tibetan Buddhism.
Milarepa 
 Milarepa, The Hundred Thousand Songs of Milarepa, translated by Garma C.C. Chang, City Lights Books, 1999,
Quinn Sullivan 
 He has studied with Brian Cass of The Overclock Orchestra and the Toe Jam Puppet Band as well as Stan Belmarce.
Quinn Sullivan 
 Sullivan first gained national media attention at age six when he appeared on The Ellen Degeneres Show.
Quinn Sullivan 
 Sullivan gained more notoriety when Buddy Guy asked him to come on stage and play during a performance at the Zeiterion Theater in New Bedford, Massachusetts, in 2007.
Quinn Sullivan 
 Quinn has since performed on stage with Guy as well as with B.B. King and has played in venues such as the Beacon Theatre in New York City, the Orpheum Theatre in Boston, and Buddy Guy’s Legends in Chicago.
Quinn Sullivan 
 In 2008, Sullivan appeared on The Oprah Winfrey Show and was featured on NBC's The Today Show in July 2009.
Quinn Sullivan 
 In 2009, Sullivan opened for Buddy Guy on his East Coast tour during the summer, played his own set at the popular summer music festival Lollapalooza, as well as the Austin City Limits Festival in October.
Quinn Sullivan 
 Sullivan makes a guest appearance on Buddy Guy’s Grammy-nominated album Skin Deep, released in 2008.
Quinn Sullivan 
 Quinn's Father's Band: "18 years on ... The PEARLY BAKER BAND keeps on truckin' " (South Coast Today)
Yellowfin tuna 
 The yellowfin tuna (Thunnus albacares) is a species of tuna found in pelagic waters of tropical and subtropical oceans worldwide.
Yellowfin tuna 
 Yellowfin is often marketed as ahi, from its name ʻahi although the name ʻahi in Hawaiian also refers to the closely related bigeye tuna.
Yellowfin tuna 
 Although the species name albacares might suggest otherwise, the fish usually known as albacore is a different species of tuna.
Malcolm Rifkind 
 He was the Chairman for the Intelligence and Security Committee and the Member of Parliament (MP) for the constituency of Kensington.
Malcolm Rifkind 
 He first became a Conservative MP at the February 1974 General Election for the constituency of Edinburgh Pentlands.
Malcolm Rifkind 
 He was first made a cabinet minister in 1979 and served constantly through 18 years of Conservative government.
Malcolm Rifkind 
 He tried but failed to regain the seat at the 2001 General Election and re-entered parliament in 2005 as the MP for Kensington.
Red wolf 
 Red wolves were declared extinct in the wild in 1980 after the few remaining wild wolves were placed in a captive breeding program.
Red wolf 
 Reintroduced to the wild in 1987 in northeastern North Carolina, red wolves began to recover, but the population is rapidly diminishing as of late 2016.
Red wolf 
 It is slender and long-legged, and it lives in the wild only on the Albemarle Peninsula in North Carolina.
Ocelot 
 Once hunted for its beautiful fur, the cat is now protected and listed as 'least concern' by the IUCN Red List.
Iteration 
 In everyday life, an iteration is simply a repeated action, for example when someone says, "Do I have to reiterate myself?".
Iteration 
 In computer science, an iteration is one run through a block of code that is repeated multiple times.
Iteration 
 In fractal geometry, an iteration is one application of the set of rules of the fractal to create another stage of the fractal.
Dennis Brain 
 His recordings include the four horn concertos by Wolfgang Amadeus Mozart which he recorded with the Philharmonia Orchestra conducted by Herbert von Karajan.
Dennis Brain 
 Several of his family were horn players, including his father Aubrey, his grandfather Alfred Edwin Brain Sr and his uncle Alfred Edwin Brain Jr.   His mother Marion was a singer who had sung at Covent Garden.
Dennis Brain 
 From there he was sent to St Paul’s School in Kensington where he sang in the choir and played piano solos at concerts.
Dennis Brain 
 In 1936 he left school and got a scholarship to the  Royal Academy of Music where he learned the horn with his father as well as the piano and, from 1938, the organ.
Dennis Brain 
 He learned a lot from his organ teacher G.D.Cunningham who had taught his uncle Alfred the piano some 40 years before.
Dennis Brain 
 Dennis’s first professional concert was at the Queen’s Hall in 1938 when he played Bach’s Brandenburg Concerto no 1 together with his father (there are important solo parts for two horns in this music).
Dennis Brain 
 He managed to get a job as principal horn with the RAF Central Band which were in Uxbridge in north-west London.
Dennis Brain 
 The older players in the band might not have liked a 17-year-old boy to have a principal’s job, but everybody realized he had exceptional skills.
Dennis Brain 
 There were lunch-hour concerts in the National Gallery during the war, and he often played in these.
Dennis Brain 
 After the war two new orchestras were formed in London: the Philharmonia and the Royal Philharmonic Orchestra.
Dennis Brain 
 He kept up his organ playing (his teacher had hoped he would become an organist) and in July 1954, again conducted by Karajan, Brain performed the organ part in a recording of the Easter hymn from Pietro Mascagni's Cavalleria rusticana.
Dennis Brain 
 In 1955 Brain became known to millions of people when he presented a radio program called The Early Horn.
Dennis Brain 
 Among the many concerts he played in was a music festival in 1956 which celebrated the life of Gerard Hoffnung, the artist who had drawn many cartoons about music.
Dennis Brain 
 The horn he played for many years had lots of dents in it because he kept knocking it or dropping it.