hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Tensor product of quadratic forms
In mathematics, the tensor product of quadratic forms is most easily understood when one views the quadratic forms as quadratic spaces. If R is a commutative ring where 2 is invertible, and if  and  are two quadratic spaces over R, then their tensor product  is the quadratic space whose underlying R-module is the tensor product  of R-modules and whose quadratic form is the quadratic form associated to the tensor product of the bilinear forms associated to  and .

In particular, the form  satisfies

(which does uniquely characterize it however). It follows from this that if the quadratic forms are diagonalizable (which is always possible if 2 is invertible in R), i.e.,

then the tensor product has diagonalization

Bilinear form
In mathematics, a bilinear form is a bilinear map V × V → K on a vector space V (the elements of which are called vectors) over a field K (the elements of which are called scalars). In other words, a bilinear form is a function B : V × V → K that is linear in each argument separately:

B(u + v, w) = B(u, w) + B(v, w)     and     B(λu, v) = λB(u, v)

B(u, v + w) = B(u, v) + B(u, w)     and     B(u, λv) = λB(u, v)

The dot product on  is an example of a bilinear form which is also an inner product. An example of a bilinear form that is not an inner product would be the four-vector product.

The definition of a bilinear form can be extended to include modules over a ring, with linear maps replaced by module homomorphisms.

When K is the field of complex numbers C, one is often more interested in sesquilinear forms, which are similar to bilinear forms but are conjugate linear in one argument.
Saturday Night Live Japan
Saturday Night Live Japan (サタデー・ナイト・ライブ JPN) was a Japanese late-night live television sketch comedy and variety television program broadcast that aired both on Fuji TV and Fuji TV NEXT. It was adaptation of Saturday Night Live on NBC that relies more on the konto style of comedy.

Glossary of owarai terms
The following glossary of words and terms (generally of Japanese origin) are related to owarai (Japanese comedy).  Many of these terms may be used in areas of Japanese culture beyond comedy, including television and radio, music. Some have been incorporated into normal Japanese speech.
Krzewica, Tomaszów Lubelski County
Krzewica [kʂɛˈvit͡sa] is a village in the administrative district of Gmina Ulhówek, within Tomaszów Lubelski County, Lublin Voivodeship, in eastern Poland, close to the border with Ukraine. The village is located in the historical region Galicia.

Lublin Voivodeship
Lublin Voivodeship (Polish: województwo lubelskie [vɔjɛˈvut͡stfɔ luˈbɛlskʲɛ] ⓘ) is a voivodeship (province) of Poland, located in the southeastern part of the country, with its capital being the city of Lublin.

The region is named after its largest city and regional capital, Lublin, and its territory is made of four historical lands: the western and central part of the voivodeship, with Lublin itself, belongs to Lesser Poland, the eastern part of Lublin Area belongs to Cherven Cities/Red Ruthenia, and the northeast belongs to Polesie and Podlasie.
Lublin Voivodeship borders Subcarpathian Voivodeship to the south, Świętokrzyskie Voivodeship to the south-west, Masovian Voivodeship to the west and north, Podlaskie Voivodeship along a short boundary to the north, Belarus (Brest Region) and Ukraine (Lviv and Volyn Regions) to the east. The region's population as of 2024 was 1,996,440. It covers an area of 25,155 square kilometres (9,712 sq mi).
Beatriz Canedo Patiño
Beatriz Canedo Patiño (1950–2016) was a Bolivian fashion designer described as the "Queen of Alpaca" due to her use of textiles from camelids such as the vicuña, alpaca, and llama. The New York Times described her in 2006 as "Bolivia's best known fashion designer."

Camelidae
Camelidae is a family of mammals belonging to the ungulate order Artiodactyla (even-toed ungulates) and the only living family in the suborder Tylopoda. The seven extant species of camelid are divided into two tribes, Camelini, including dromedary camels, Bactrian camels and wild Bactrian camels, and Lamini, including llamas, alpacas, vicuñas, and guanacos.
Greater rhea
The greater rhea (Rhea americana) is a species of flightless bird native to eastern South America. Other names for the greater rhea include the grey, common, or American rhea; ema (Portuguese); or ñandú (Guaraní and Spanish). One of two species in the genus Rhea, in the family Rheidae, it inhabits a variety of open areas, such as grasslands, savanna or grassy wetlands. Weighing 20–27 kilograms (44–60 lb), the greater rhea is the largest native bird in the Americas. In the wild, the greater rhea has a life expectancy of 10.5 years. It is also notable for its reproductive habits, and for the fact that a population has established itself in Northern Germany in recent years. The species is listed as Near Threatened by the IUCN.

Northern Germany
Northern Germany (German: Norddeutschland, [ˈnɔʁtdɔɪ̯tʃlant] ⓘ) is a linguistic, geographic, socio-cultural and historic region in the northern part of Germany which includes the coastal states of Schleswig-Holstein, Mecklenburg-Vorpommern and Lower Saxony and the two city-states Hamburg and Bremen. It contrasts with Southern Germany, Western Germany, and Eastern Germany.
James William Baskin
James William Baskin (January 4, 1920 – January 8, 1999) was a Canadian politician, businessman and lumberman. He was elected to the House of Commons of Canada as a Member of the Progressive Conservative Party to represent the riding of Renfrew South in the 1957 federal election. He was re-elected in 1958 and 1962.

The son of James Robert Baskin and Ethel Gill, he was educated in Norwood. In 1940, he married Gladys L. Scott. Baskin operated a wholesale lumber business in Renfrew.

He lost in the elections of 1963, 1965 and 1968, the latter in which he was a candidate for the riding of Lanark and Renfrew. Prior to his federal political experience, he served in World War II in the Royal Canadian Air Force for five years.

Renfrew, Ontario
Renfrew is a town on the Bonnechere River in Renfrew County, Ontario, Canada. Located one hour west of Ottawa in Eastern Ontario, Renfrew is the fourth largest town in the county after Petawawa, Pembroke and Arnprior. The town is a small transportation hub connecting Highway 60 and Highway 132 with the Trans-Canada Highway. Renfrew is also known historically for its role in the formation of the National Hockey League. It lies about 5 kilometres from the Quebec border, about 10 kilometres by road. Renfrew makes most of Canada’s hockey tape.
Hypothenar hammer syndrome
Hypothenar hammer syndrome (HHS) is a vascular occlusion in humans in the region of the ulna. It is caused by repetitive trauma to the hand or wrist (such as that caused by the use of the hand as a hammer) by the vulnerable portion of the ulnar artery as it passes over the hamate bone, which may result in thrombosis, irregularity or aneurysm formation. HHS is a potentially curable cause of Raynaud's syndrome, distinct from hand–arm vibration syndrome.

Ulnar artery
The ulnar artery is the main blood vessel, with oxygenated blood, of the medial aspects of the forearm.  It arises from the brachial artery and terminates in the superficial palmar arch, which joins with the superficial branch of the radial artery.  It is palpable on the anterior and medial aspect of the wrist.

Along its course, it is accompanied by a similarly named vein or veins, the ulnar vein or ulnar veins.

The ulnar artery, the larger of the two terminal branches of the brachial, begins a little below the bend of the elbow in the cubital fossa, and, passing obliquely downward, reaches the ulnar side of the forearm at a point about midway between the elbow and the wrist. It then runs along the ulnar border to the wrist, crosses the transverse carpal ligament on the radial side of the pisiform bone, and immediately beyond this bone divides into two branches, which enter into the formation of the superficial and deep volar arches.
James Redmond (artist)
James McKay Redmond (September 14, 1901 – December 21, 1944) was an American painter, muralist, and printmaker active in Los Angeles in the 1920s and 1930s. His prismatic colors and sinuous lines were admired by the critics of his day and his New Deal-era murals are considered particularly fine exemplars of the genre. A leader in the local art community, he succeeded his mentor Stanton Macdonald-Wright as a director of the progressive and influential Art Students League of Los Angeles and steered the organization through the Great Depression. During World War II, he enlisted in the U.S. Army, and landed at Omaha Beach in Normandy, France on D-Day with his battalion of combat engineers. Redmond was killed in action four days before Christmas 1944 during the German counteroffensive into the Ardennes Forest known as the Battle of the Bulge.

New Deal artwork
New Deal artwork is an umbrella term used to describe the creative output organized and funded by the Roosevelt administration's New Deal response to the Great Depression. This work produced between 1933 and 1942 ranges in content and form from Dorothea Lange's photographs for the Farm Security Administration to the Coit Tower murals to the library-etiquette posters from the Federal Art Project to the architecture of the Solomon Courthouse in Nashville, Tennessee. The New Deal sought to "democratize the arts" and is credited with creating a "great body of distinguished work and fostering a national aesthetic."
Seret Scott
Seret Scott (/səˈrɛt/; born September 1, 1949) is an American actress, director, and playwright, best known for her roles in the films Losing Ground and Pretty Baby, as well as guest appearances on the televisions shows The Equalizer, Miami Vice, and Cosby. She is also known for her theatrical roles on Broadway and the many plays she has directed on national and regional stages.

Seret Scott directed The Old Settler by John Henry Redwood at The Studio Theatre in Washington, D.C., in 1997.

Studio Theatre (Washington, D.C.)
The Studio Theatre is a non-profit theater production company located in the 14th Street corridor of Washington, D.C. It produces contemporary plays in a four-stage complex. Stages include the Metheny, the Mead and Milton, and Stage 4, a black box.
VP-26 (1944–1946)
VP-26 was a Patrol Squadron of the U.S. Navy. The squadron was established as Patrol Squadron 26 (VP-26) on 1 May 1944, redesignated Patrol Bombing Squadron 26 (VPB-26) on 1 October 1944, redesignated Patrol Squadron 26 (VP-26) on 15 May 1946 and disestablished on 14 December 1946. It was the second squadron to be designated VP-26, the first VP-26 was redesignated VP-14 on 1 July 1941.

Naval Station Norfolk
Naval Station Norfolk is a United States Navy base in Norfolk, Virginia, that is the headquarters and home port of the U.S. Navy's Fleet Forces Command. The installation occupies about 4 miles (6.4 km) of waterfront space and 11 miles (18 km) of pier and wharf space of the Hampton Roads peninsula known as Sewell's Point.  It is the world's largest naval station, with the largest concentration of U.S. Navy forces through 75 ships alongside 14 piers and with 134 aircraft and 11 aircraft hangars at the adjacently operated Chambers Field. Port Services controls more than 3,100 ships' movements annually as they arrive and depart their berths.

Air Operations conducts over 100,000 flight operations each year, an average of 275 flights per day or one every six minutes. Over 150,000 passengers and 264,000 tons of mail and cargo depart annually on Air Mobility Command (AMC) aircraft and other AMC-chartered flights from the airfield's AMC Terminal.
Ruacana
Ruacana is a town in the Omusati Region of northern Namibia and the district capital of the Ruacana electoral constituency. It is located on the border with Angola on the river Kunene. The town is known for the picturesque Ruacana Falls nearby, and for the Ruacana Power Station. Ruacana had a population of 5,939 people in 2023.

SWAPO
The South West Africa People's Organisation (SWAPO /ˈswɑːpoʊ/; Afrikaans: Suidwes-Afrikaanse Volks Organisasie, SWAVO; German: Südwestafrikanische Volksorganisation, SWAVO), officially known as the SWAPO Party of Namibia, is a political party and former independence movement in Namibia (formerly South West Africa). Founded in 1960, it has been the governing party in Namibia since the country achieved independence in 1990. The party continues to be dominated in number and influence by the Ovambo ethnic group.

SWAPO held a two-thirds majority in parliament from 1994 to 2019. In the general election held in November 2019, the party won 65.5% of the popular vote and 63 out of the 104 seats in the National Assembly. It also holds 28 out of the 42 seats in the National Council. From November 2017 until his death in February 2024, Namibian President Hage Geingob remained the president of SWAPO after being elected to the position at the party's electoral congress.
Nana Mchedlidze
Nana Mchedlidze (Georgian: ნანა მჭედლიძე, Russian: Нана  Мчедлидзе; 20 March 1926 – 29 March 2016) was a Soviet and Georgian actress, film director and screenwriter.

From 1950 to 1954 she was an actress with the Tbilisi Rustaveli Theatre. After 1957 she was the director of the film studio Georgia-Film.

She became a People's Artist of the Georgian SSR  in 1983.

Georgian Film Studio
Georgian Film Studio (Georgian: ქართული ფილმი, kartuli pilmi; Russian: Грузия-фильм; Gruziya-Fil'm) is one of world's oldest film studios that has produced 800 features, made-for-TV and short films, 600 documentaries, and 300 animation movies. During Soviet times, the studio was one of the most active places for film production. Having grown organically from the merger of several film production companies that operated in the beginning of the twentieth century in Tbilisi, the studio had been renamed several times before becoming Georgian Film (Gruziya-Film in Russian) in 1953. Sitting on 9.75 hectares (24 acres) of prime land in Tbilisi, Georgian Film Studios offers several sound stages, recording and editing facilities, various production services, modern equipment and professional crews. Georgian Film was founded in 1921.
Buster Brown suit
A Buster Brown suit was a very popular style of clothing for young boys in the United States during the early 20th century. It was named after the comic strip character Buster Brown, created in 1902 by Richard Felton Outcault.

It typically consisted of a belted, double-breasted tunic or jacket worn with a large round collar, floppy bow, and shorts or knickerbockers. It was often worn with a round straw hat and a haircut with bangs. Along with the sailor suit, the Eton suit, the Norfolk suit and the Fauntleroy suit, the Buster Brown suit is cited as one of the key looks in boys' clothing of the period.

Richard F. Outcault
Richard Felton Outcault (/ˈaʊtkɔːlt/; January 14, 1863 – September 25, 1928) was an American cartoonist. He was the creator of the series The Yellow Kid and Buster Brown and is considered a key pioneer of the modern comic strip.
2015 Seguros Bolívar Open Medellín – Men's singles
Austin Krajicek was the defending champion, but chose to compete in the Japan Open instead of defending his title.

Paolo Lorenzi won the title defeating Gonzalo Lama in the final, 7–6(7–3), 2–0 retired.

Gonzalo Lama
Gonzalo Andrés Lama Feliu (Latin American Spanish: [ɡonˈsalo ˈlama]; born 27 April 1993 in Santiago) is a former Chilean professional tennis player. His best singles ranking was 160 in June 2016. He won two Challengers (Cali and São Paulo), along with fourteen futures, twelve in singles and two in doubles.
Blue Duster
Blue Duster was an American-bred, British-trained champion Thoroughbred racehorse. She was named European Champion Two-year-old Filly in the Cartier Racing Awards for 1995 and was the highest rated juvenile filly in the International Classification. In her championship season Blue Duster was unbeaten in four races including the Group One Cheveley Park Stakes, the Group Three Princess Margaret Stakes and the Group Three Queen Mary Stakes.

Queen Mary Stakes
The Queen Mary Stakes is a Group 2 flat horse race in Great Britain open to two-year-old fillies. It is run at Ascot over a distance of 5 furlongs (1,006 metres), and it is scheduled to take place each year in June.

The event is named after Mary of Teck. It was established in 1921, and the inaugural running was won by Wild Mint.

The present system of race grading was introduced in 1971, and for a period the Queen Mary Stakes was classed at Group 3 level. It was promoted to Group 2 status in 2004. The Queen Mary Stakes is now staged on day two of the five-day Royal Ascot meeting.
A Little Bit Alexis
"A Little Bit Alexis" is a song performed by Annie Murphy as Alexis Rose on the Canadian sitcom, Schitt's Creek. The song first appeared in the eighth episode of the fifth season, "The Hospies", and was later released commercially as an independent single on February 27, 2019. Partial proceeds from the song were donated to MusiCounts, a Canadian organization providing music resources to schools in need.

Annie Murphy
Anne Frances Murphy (born December 19, 1986) is a Canadian actress. She rose to prominence for her starring role as Alexis Rose in the sitcom Schitt's Creek (2015–2020), for which she received a Primetime Emmy Award, as well as nominations for a Golden Globe Award and two Critics' Choice Television Awards.

Murphy has since starred in the comedy-drama series Kevin Can F**k Himself (2021–2022), Russian Doll (2022), and the episode "Joan Is Awful" of the anthology series Black Mirror (2023), with the lattermost winning her a Critics' Choice Super Award. She had a voice role in the animated film Ruby Gillman, Teenage Kraken (2023).
Nkwanta North District
Nkwanta North District (French: Nkwanta Nord) is one of the nine (9)  districts in Oti Region, Ghana. Originally it was formerly part of the then-larger Nkwanta District on 10 March 1989, until the northern part of the district was split off to create Nkwanta North District on 29 February 2008, which was established by Legislative Instrument (L.I.) 1846; thus the remaining part has been renamed to become Nkwanta South District, which was later elevated to municipal district assembly status on 14 November 2017 (effectively 15 March 2018) to become Nkwanta South Municipal District; which was established by Legislative Instrument (L.I.) 2283. The district assembly is located in the northern part of Oti Region and has Kpassa as its capital town.

Oti Region
The Oti Region is one of the six newly created regions of Ghana and was carved out of the Volta Region in December 2018. This followed the campaign promise of Nana Akufo-Addo to create new regions in order to bring governance closer to the people. The region was inaugurated on May 14, 2019 with Dambai as its capital.
Square One Bus Terminal
Square One Bus Terminal is a GO Transit intercity bus terminal located in central Mississauga, Ontario, Canada. It is situated directly across Rathburn Road West from the City Centre Transit Terminal (the main hub for local MiWay bus service and a stop on the Mississauga Transitway) and Square One Shopping Centre, after which the terminal is named.

Routes stopping at the terminal include: off-peak bus service along the Milton GO Train corridor from downtown Toronto; Mississauga to Finch Bus Terminal; Mississauga to Guelph; Hamilton to Richmond Hill; Highway 407 West routes; and routes connecting Waterloo Region to Greater Toronto.

Services will also connect to the planned Hurontario LRT on Hurontario Street.

Pickering GO Station
Pickering GO Station is a train and bus station in the GO Transit network located in Pickering, Ontario, Canada. It is a stop on the Lakeshore East line and was the eastern terminus from 1967 until 1990, when service was extended to Whitby and subsequently to Oshawa.
Oleksandr Batyuk
Oleksandr Mykhailovych Batyuk (Ukrainian: Олекса́ндр Миха́йлович Батю́к; born 14 January 1960) is a former Soviet cross-country skier who competed in the 1980s, training at Dynamo in Chernihiv. He won a silver in the 4 × 10 km relay at the 1984 Winter Olympics in Sarajevo. He is a member of the Ski Federation of Ukraine and the only Olympian of the federation who received medal at Olympics.

Batyuk also won two medals in the 4 × 10 km relay at the FIS Nordic World Ski Championships with a gold in 1982 (tied with Norway) and a silver in 1987.

His best individual finish was sixth twice in the World Cup (1984, 1986).

He was born in Chernihiv, Soviet Union.

FIS Nordic World Ski Championships
The FIS Nordic World Ski Championships is a biennial Nordic skiing event organized by the International Ski Federation (FIS). The World Championships was started in 1924 for men and opened for women's participation in 1954. World Championship events include Nordic skiing's three disciplines: cross-country skiing, ski jumping, and Nordic combined (the latter being a combination sport consisting of both cross-country and ski jumping). The Winter Olympics from 1924 to 1980 were also the Nordic World Ski Championships. This meant that the Olympic champions were also World champions and received an additional medal from the International Ski Federation (FIS). Since 1985, the World Championships have been held in odd-numbered years.
M Telus (concert hall)
The M Telus (formerly known as Métropolis) is a performing arts centre in Montreal, Quebec, Canada. It is located in the central part of the  downtown core, on Saint Catherine Street East between Saint-Dominique and De Bullion Streets, in the Quartier des Spectacles. The hall primarily features rock music groups, and is a venue for several festivals, including the Montreal International Jazz Festival and the FrancoFolies de Montréal.

It can accommodate up to 2,350 people. The venue is within walking distance from Place-des-Arts Metro station, the Complexe Desjardins in the west and from the Saint-Laurent metro station. In 2011, the venue was ranked as the ninth most popular club venue worldwide in ticket sales.

In 2016, naming rights were acquired by Telus. The telecommunications company plans to invest $5 million in improvements to the club over the next decade, as part of its corporate rebranding effort.

Performing arts center
Performing arts center/centre (see spelling differences), often abbreviated as PAC, is usually a complex housing performance spaces for various performing arts, including dance, music, and theatre. In some cases it refers to a single multi-use space, or alternatively, to a performing arts college.
Iron Chef Gauntlet
Iron Chef Gauntlet is a television series on Food Network that began airing on April 16, 2017. The series is a reboot of the Iron Chef and Iron Chef America series that gained popularity on Food Network and is hosted by Alton Brown, who also takes over as the series' Chairman. Seven chefs from around the country battle each other in an elimination contest, with the last chef remaining then facing a "gauntlet" challenge of defeating three other Iron Chefs in order to earn the title of Iron Chef. In the first season, the Iron Chefs forming the Gauntlet were Bobby Flay, Masaharu Morimoto, and Michael Symon. The second season of Iron Chef Gauntlet began airing April 4, 2018 and was scheduled for six episodes. The Gauntlet Iron Chefs for the second season were Alex Guarnaschelli, Gauntlet season one winner Stephanie Izard, and Michael Symon.

Bobby Flay
Robert William Flay (born December 10, 1964) is an American celebrity chef, food writer, restaurateur, and television personality. Flay is the owner and executive chef of several restaurants and franchises, including Bobby's Burger Palace, Bobby's Burgers, and Amalfi. He has appeared on Food Network since 1995, which won him four Daytime Emmy Awards and a star on the Hollywood Walk of Fame.