hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Singular matrix
A singular matrix is a square matrix that is not invertible, unlike non-singular matrix which is invertible. Equivalently, an -by- matrix  is singular if and only if determinant, . In classical linear algebra, a matrix is called non-singular (or invertible) when it has an inverse; by definition, a matrix that fails this criterion is singular. In more algebraic terms, an -by- matrix A is singular exactly when its columns (and rows) are linearly dependent, so that the linear map  is not one-to-one.

In this case the kernel (null space) of A is non-trivial (has dimension ≥1), and the homogeneous system  admits non-zero solutions. These characterizations follow from standard rank-nullity and invertibility theorems: for a square matrix A,  if and only if , and  if and only if .

Triviality (mathematics)
In mathematics, the adjective trivial is often used to refer to a claim or a case which can be readily obtained from context, or a particularly simple object possessing a given structure (e.g., group, topological space). The noun triviality usually refers to a simple technical aspect of some proof or definition. The origin of the term in mathematical language comes from the medieval trivium curriculum, which distinguishes from the more difficult quadrivium curriculum. The opposite of trivial is nontrivial, which is commonly used to indicate that an example or a solution is not simple, or that a statement or a theorem is not easy to prove.

Triviality does not have a rigorous definition in mathematics. It is subjective, and often determined in a given situation by the knowledge and experience of those considering the case.
Kidnapping, Caucasian Style!
Kidnapping, Caucasian Style! (Russian: Кавказская пленница!; informally referred to as the Kidnapping, Caucasian Style 2 version) is a Russian comedy film by director Maxim Voronkov. A remake of the 1967 film of the same name, the plot revolves around bride kidnapping, an old tradition that used to exist in certain regions of the North Caucasus.

Dedicated to the memory of Ilya Oleynikov, the film premiered on August 21, 2014. As was the case with the original, filming was done in the Crimea, not in the North Caucasus. The movie was met with strongly negative reviews in the Russian media, with some considering it being one of the worst films made to date, and it was a box-office bomb.

Ilya Oleynikov
Ilya Lvovich Oleynikov (Russian: Илья Львович Олейников; born Ilya Lvovich Klyaver (Клявер); 10 July 1947 – 11 November 2012) was a Russian comic actor and television personality, TEFI winner (1996, 2001), People's Artist of Russia (2001).
Reginald Parkin
Reginald Henry Parkin (25 July 1909 – 16 April 1994) was an English cricketer active from 1931 to 1939 who played for Lancashire. He was born in Tunstall and died in Stockport. He appeared in 21 first-class matches as a righthanded batsman who bowled right arm off break. He scored 286 runs with a highest score of 60 and held four catches. He took 23 wickets with a best analysis of three for 52.

Wicket
In the sport of cricket, the term wicket has several meanings:

It is either of the two sets of three stumps and two bails at each end of the pitch. The fielding team's players can hit the wicket with the ball in a number of ways to get a batter out. 
The wicket is guarded by a batter who, with their bat (and sometimes with their pads, but see the laws on LBW, leg before wicket), attempts to prevent the ball from hitting the wicket (if it does, they may be bowled) and to score runs where possible.

Through metonymic usage, the dismissal of a batter is known as the taking of a wicket.

The cricket pitch itself is sometimes referred to as the wicket.
Richmond Heights station
Richmond Heights station is a light rail station on the Blue Line of the St. Louis MetroLink system. This at-grade station is located near the interchange of Interstate 170 and Galleria Parkway in Richmond Heights, Missouri.

The station has a small commuter parking lot with 57 spaces and includes a kiss and ride turnaround.

Interstate 170
Interstate 170 (I-170), also known as the Inner Belt Expressway, is an 11.17-mile (17.98 km) north–south auxiliary Interstate Highway in Greater St. Louis, Missouri. I-170 connects to I-270 at its northern terminus and I-64 at its southern terminus. I-170 crosses its parent, I-70, near St. Louis Lambert International Airport.
David Fales
David Daniel Fales (born October 4, 1990) is an American former professional football player who was a quarterback in the National Football League (NFL). He was selected by the Chicago Bears in the sixth round of the 2014 NFL draft. He played college football for the San Jose State Spartans.

Fales played high school football at Palma School in Salinas, California. After redshirting freshman year for the Nevada Wolfpack of the University of Nevada, Reno, Fales attended Monterey Peninsula College for two years and transferred to San Jose State University for his junior year in 2012. With Fales, the Spartans went 11–2 in 2012 with the school's first-ever BCS ranking, first AP Poll ranking since 1975, and first bowl game berth since 2006. With 31 touchdown passes in his first year with San Jose State, Fales was the most accurate FBS quarterback for the 2012 season and was MVP of the 2012 Military Bowl.

Colorado State Rams football
The Colorado State Rams football program represents Colorado State University and is a member of the NCAA Division I Football Bowl Subdivision and the Mountain West Conference. The Rams have long-standing rivalries with Colorado, Wyoming, and Air Force. The team is currently led by interim head coach and defensive coordinator Tyson Summers, who was named interim head coach after Jay Norvell was fired on October 19, 2025. UConn Huskies football head coach Jim Mora will serve has head coach at the start of the 2026 season.

The Rams have played their home games at Canvas Stadium since 2017. Previously, the team played 49 seasons (1968–2016) at Sonny Lubick Field at Hughes Stadium. The first game at Canvas Stadium (known as Colorado State Stadium for the 2017 season only) was played on August 26, 2017, when the Rams defeated the Oregon State Beavers 58–27.
Gideon's Corpse
Gideon's Corpse is a thriller novel by Douglas Preston and Lincoln Child. The book was released on January 10, 2012, by Grand Central Publishing. The book centers around Gideon Crew and is a sequel to Gideon's Sword. The plot focuses on a nuclear scare, the federal reaction, and Gideon's attempts to unravel the mystery.

Grand Central Publishing
Grand Central Publishing is a book publishing imprint of Hachette Book Group, originally established in 1970 as Warner Books when Kinney National Company acquired the New York City-based Paperback Library. When Time Warner sold their book publishing business to Hachette Livre in March 2007, the North American operations of the Time Warner Book Group were renamed Hachette Book Group, while the group's Warner Books imprint became Grand Central Publishing, named in part by the proximity of their new offices to New York's Grand Central Terminal.

In addition to the Grand Central imprint itself, Grand Central Publishing has several sub-imprints, including Balance, Forever/Forever Yours, Legacy Lit, and Twelve.
Pandabeswar
Pandabeswar (also spelled Pandaveswar) is a neighborhood, a community development block and an administrative centre in Pandabeswar CD Block in the city of Durgapur of Paschim Bardhaman district in the state of West Bengal, India.

Pandaveswar Area
Pandaveswar Area is one of the 14 operational areas of the Eastern Coalfields Limited located mostly in the Durgapur subdivision of Paschim Bardhaman district with a spread over to the Suri Sadar subdivision of Birbhum district, across the Ajay, in the state of West Bengal, India.
Kirkby train crash
On 13 March 2021, a Class 507 train operated by Merseyrail collided with the buffer stops at Kirkby railway station in Merseyside, England. The train had passed the start of the 15 mph (24 km/h) speed restriction for the station whilst coasting at 41 mph (66 km/h). The driver later applied the emergency brakes, but the train still collided with the buffer stop at 29 mph (47 km/h).

The only person injured was the driver of the train, Phillip Hollis, who was found to have been distracted by using his mobile phone before the crash. He was dismissed from Merseyrail and later prosecuted, pleading guilty to a charge of endangering the safety of people on the railway, for which he received a 12-month suspended sentence. The Rail Accident Investigation Branch investigated the accident and made recommendations including researching systems to measure driver alertness and further assessing the risk of buffer stop collisions on the Merseyrail network.

Merseyside Fire and Rescue Service
Merseyside Fire and Rescue Service is the statutory fire and rescue service covering the county of Merseyside in north-west England and is the statutory Fire and Rescue Authority responsible for all 999 fire brigade calls in Sefton, Knowsley, St. Helens, Liverpool and Wirral.
2022–23 Merrimack Warriors men's ice hockey season
The 2022–23 Merrimack Warriors Men's ice hockey season was the 67th season of play for the program, the 34th at the Division I level, and the 34th in the Hockey East conference. The Warriors represented Merrimack College and were coached by Scott Borek, in his 5th season.

2022–23 Hockey East men's season
The 2022–23 Hockey East men's season was the 39th season of play for Hockey East and took place during the 2022–23 NCAA Division I men's ice hockey season. The season began on October 1, 2022 and concluded on April 6, 2023.
Frøken Kirkemus
Frøken Kirkemus (lit. Miss Churchmouse) is a 1941 Danish family film directed by Lau Lauritzen Jr. and Alice O'Fredericks starring Marguerite Viby. The film was remade in Sweden the same year (as Fröken Kyrkråtta), directed by Schamyl Bauman, again with Viby in the lead role. The film is an adaptation of Ladislas Fodor's play A templon egére, which was adapted into an English play titled A Church Mouse by Benn Levy in 1931 and then an American film, Beauty and the Boss, by Roy del Ruth in 1932.

Benn Levy
Benn Wolfe Levy (7 March 1900 – 7 December 1973) was a Labour Party Member of Parliament in the House of Commons (1945–1950), and a successful playwright. He was educated at Repton School and University College, Oxford and served in uniform in both World Wars.
Salsas Fresh Mex
Salsas Fresh Mex is an Australian chain of fast-food restaurants. It serves a variety of Tex-Mex foods including tacos, burritos, quesadillas, nachos, other specialty items, and a variety of "value menu" items.

Salsas was founded by Lawrence Di Tomasso (now owner of Laurie Dee's), it was sold in 2009 to Retail Zoo.

There are 42 locations in operation across Australia.

Quesadilla
A quesadilla (/ˌkeɪsəˈdiːjə/; Spanish: [kesaˈðiʝa] ⓘ; Spanish diminutive of quesada) is a Mexican dish made from a tortilla folded in half or two tortillas that are filled with cheese (queso), and sometimes meats, spices, and other fillings, and then cooked on a griddle or stove. Traditionally, corn tortillas are used, but the dish can also be made with flour tortillas. Quesadillas are frequently sold at Mexican restaurants all over the world.
The West of the Imagination
The West of the Imagination is a six-part documentary series that aired weekly on PBS from September 22, 1986 to October 27, 1986. The series captured the story of the American "Wild West" as it was told through art, film, photography, music, and entertainers within broader pop culture. Created by Dr. William H. Goetzman and hosted by James Whitmore, The West of the Imagination was produced for PBS by KERA-TV, in association with the Independent Communications Association of Los Angeles and London. Alongside the series, W.W. Norton published a companion book, written by creator William H. Goetzmann.

William H. Goetzmann
William Harry Goetzmann (July 20, 1930 – September 7, 2010) was an American historian and emeritus professor in the American Studies and American Civilization Programs at the University of Texas at Austin. He attended Yale University as a graduate student and was friends with Tom Wolfe while there. His work on the American West won him the highest prizes for historians, the Parkman Prize and the Pulitzer Prize. He has written and published extensively on American philosophy, American political history, and the American arts.  An advocate for the importance of history as a public discussion, he has served in various capacities in television and film production, notably for PBS. He was most recently the Jack S. Blanton Sr. Chair Emeritus in History and American Studies.  His last book published during his lifetime was Beyond the Revolution:  A History of American Thought From Paine to Pragmatism (2009).
James Baley
James Baley is a Canadian singer and dancer from Toronto, Ontario, whose debut album A Story was released in 2021.

A longtime figure in Toronto's ballroom culture scene, Baley first became known as a musician when he contributed vocals to Azari's 2018 single "Gotasoul", which was a Juno Award nominee for Dance Recording of the Year at the Juno Awards of 2019. In 2020 he was a featured vocalist on "Champagne", a single from July Talk's Juno-winning album Pray for It, and has also been a guest vocalist with U.S. Girls, Zaki Ibrahim and Badge Époque Ensemble.

He released A Story in 2021, and promoted the album with an "immersive" live show at Toronto's Great Hall on October 22, which blended live music, ballroom performance and multimedia elements.

In 2022, Baley and filmmaker Kyisha Williams created a performance video for the ballroom competition series CBX: Canadian Ballroom Extravaganza.

He is out as gay.

Pray for It
Pray for It is the third full-length album by Canadian indie rock band July Talk, released July 10, 2020 on Sleepless Records. The album won the Juno Award for Alternative Album of the Year at the Juno Awards of 2021, and Cosette Schulz's video for "Governess Shadow" was longlisted for the 2021 Prism Prize.

In 2023 Brittany Farhat released the concert/documentary film July Talk: Love Lives Here, which profiled the band's attempts to mount a drive-in concert tour to support the album during the COVID-19 pandemic in Canada.
Francis Halliwell
Christianity portal

Francis Derrick Procter Halliwell was Archdeacon of Bombay from 1963 until 1965.

Halliwell was educated at Durham University and St Augustine's College, Canterbury; and ordained in 1937.  After a curacy in New Eltham he was Chaplain at Hubli then Colaba before his time as Archdeacon and Vicar of Lee on the Solent afterwards.

Colaba
Colaba ([koˈlaːbaː]; or ISO: Kolābā) is a part of the city of Mumbai, India. It is one of the four peninsulas of Mumbai while the other three are Worli, Bandra and Malabar Hill. During the Portuguese rule in the 16th century, the island was known as Kolbhat. After the British took over the island in the late 17th century, it was known as Kolio.
Chojna, Gmina Sulęczyno
Chojna [ˈxɔi̯na] is a village in the administrative district of Gmina Sulęczyno, within Kartuzy County, Pomeranian Voivodeship, in northern Poland.

For details of the history of the region, see History of Pomerania.

Kartuzy County
Kartuzy County (Polish: powiat kartuski; Kashubian: kartësczi pòwiat) is a county in the Pomeranian Voivodeship, Poland, with administrative seat and largest town being Kartuzy.

It came into being on 1 January 1999, as a result of the Polish local government reforms passed in 1998. The only other town in the county is Żukowo. The county covers an area of 1,120.04 square kilometres (432.4 sq mi). As of 2019 its total population is 137,942, out of which the population of Kartuzy is 14,536, that of Żukowo is 6,691, and the rural population is 116,715.

Kartuzy County on a map of the counties of Pomeranian Voivodeship

Kartuzy County is bordered by Wejherowo County to the north, the city of Gdynia to the north-east, the city of Gdańsk and Gdańsk County to the east, Kościerzyna County to the south, Bytów County to the west, and Lębork County to the north-west.
Glyphus
Glyphus is a genus of shrimp from the family Pasiphaeidae, first described by Henri Filhol in 1884. The type species is Glyphus marsupialis, by monotypy.

In La vie au fonds des mers, Filhol describes it as being found at depths of 882 m between the Canaries and Cap Vert.

Henri Filhol
Henri Filhol (13 May 1843 – 28 April 1902) was a French medical doctor, malacologist and naturalist born in Toulouse. He was the son of Édouard Filhol (1814-1883), curator of the Muséum de Toulouse.

After receiving his early education in Toulouse, he moved to Paris, where he obtained doctorates in medicine and science. In 1879 he was appointed professor of zoology at the Faculty of Toulouse. From 1894 to 1902 he occupied the chair of comparative animal anatomy at the Muséum national d'Histoire naturelle in Paris. In 1897 he became a member of the Académie des sciences.

In the field of paleontology, he performed important studies of fossilized mammals in the phosphorites in Quercy.

He served as the expedition doctor and naturalist on the French 1874 Transit of Venus Expedition to Campbell Island, with Filhol Peak on the island being named after him. In 1883 with Alphonse Milne-Edwards, Léon Vaillant, Edmond Perrier and others, he embarked on a scientific journey aboard the Talisman.
VDF
VDF may be an acronym for:

VHF Direction Finder

Venda Defence Force

Virginia Defense Force

Visual DataFlex a Fourth-generation programming language now known simply as DataFlex.

FAA LID for: Tampa Executive Airport (formerly known as Vandenberg Airport)

Vinylidene difluoride, see: 1,1-Difluoroethylene

Verifiable Delay Function, in cryptography

Venda Defence Force
The Venda Defence Force (VDF) was established in September 1982 from the 112 Battalion of the South African Defence Force and the military branch of the Venda National Force which itself had been formed when the Venda homeland became independent from South Africa in September 1979.
Mayflower Manor Apartments
Mayflower Manor Apartments is a high-rise residential building located at 263 South Main Street in Downtown Akron, Ohio, United States. It has 16 floors (as well as one sub-level) and stands at a height of 207 feet, making it one of the tallest buildings in the city.

Residential area
A residential area is a land used in which housing predominates, as opposed to industrial and commercial areas.

Housing may vary significantly between, and through, residential areas. These include single-family housing, multi-family residential, or mobile homes. Zoning for residential use may permit some services or work opportunities or may totally exclude business and industry. It may permit high density land use or only permit low density uses.  Residential zoning usually includes a smaller FAR (floor area ratio) than business, commercial or industrial/manufacturing zoning. The area may be large or small.
Operation Osprey
Operation Osprey ("Unternehmen Fischadler" in German) was a plan conceived by the German Foreign Ministry and Abwehr II. mid-1942. The plan was an enlargement of Operation Whale ("Unternehmen Wal" in German).  Planning took place in the context of American troops landing in Northern Ireland 26 January 1942, and Hitler's immediate fears surrounding this.

Ministry of foreign affairs
In many countries, the ministry of foreign affairs (abbreviated as MFA or MOFA) is the highest government department exclusively or primarily responsible for the state's foreign policy and relations, diplomacy, bilateral, and multilateral relations affairs as well as for providing support, including consular services, for a country's citizens who are abroad. The entity is usually headed by a foreign minister or minister of foreign affairs (the title may vary, such as a secretary of state who has the same functions). The foreign minister typically reports to the head of government (such as prime minister or president).
Conrad Clar
Conrad Clemens Clar or Konrad Clar (22 February 1844 – 13 January 1904) was an Austrian physician, balneologist and geologist. An innovation of a head mounted mirror and lamp for examining the throats of patients was named after him and the term "Clar (ENT) mirror" is still sometimes in use.

Balneotherapy
Balneotherapy (Latin: balneum "bath") is a pseudoscientific method of treating diseases by bathing, a traditional medicine technique usually practiced at spas. Since ancient times, humans have used hot springs, public baths and thermal medicine for therapeutic effects. While it is considered distinct from hydrotherapy, there are some overlaps in practice and in underlying principles. Balneotherapy may involve hot or cold water, massage through moving water, relaxation, or stimulation. Many mineral waters at spas are rich in particular minerals such as silica, sulfur, selenium, and radium. Medicinal clays are also widely used, a practice known as 'fangotherapy'.
Concession stand
A concession stand, or refreshment stand (American English, Canadian English), snack kiosk or snack bar (British English, Irish English) is a place where patrons can purchase snacks or food at a cinema, amusement park, zoo, aquarium, circus, fair, stadium, beach, swimming pool, concert, sporting event, or other entertainment venue. Some events or venues contract the right to sell food to third parties.  Those contracts are often referred to as a concession, hence the name for a stand where food is sold. Usually prices for goods at concession stands are greater than elsewhere for the convenience of being close to an attraction and thus often contribute significant revenue to the venue operator (especially in the case of movie theaters). Additionally, outside food and drink is often prohibited to incentivise spending at the concession stands.

Convenience
Convenient procedures, products and services are those intended to increase ease in accessibility, save resources (such as time, effort and energy) and decrease frustration. A modern convenience is a labor-saving device, service or substance which make a task easier or more efficient than a traditional method. Convenience is a relative concept, and depends on context. For example, automobiles were once considered a convenience, yet today are regarded as a normal part of life.

Because differences in lifestyles around the world, the term is a relative term based upon the conveniences previously available to a person or group.  For instance, an American definition of 'modern convenience' is likely different from that of an individual living in a developing country. Most of the time, the term 'modern convenience' is used to express personal lifestyle and home life.
Ryōsuke Oguma
Ryōsuke Oguma (小熊凌祐, born August 11, 1990, in Moroyama, Saitama, Saitama Prefecture) is a Japanese former professional baseball pitcher who is currently a staff for Chunichi Dragons of the Nippon Professional Baseball. He has played in NPB for the Dragons.

Moroyama, Saitama
Moroyama (毛呂山町, Moroyama-machi) is a town located in Saitama Prefecture, Japan. As of 1 January 2021, the town had an estimated population of 33,178 in 15,888 households and a population density of 970 persons per km2. The total area of the town is 34.07 square kilometres (13.15 sq mi).
Steve Kirsch
Steven Todd Kirsch (born 1956 in Los Angeles) is an American entrepreneur. He has started several companies and was one of two independent inventors of the optical mouse. Kirsch has been both a philanthropic supporter of medical research, and a promoter of misinformation about COVID-19 vaccines.

Multiple discovery
The concept of multiple discovery (also known as simultaneous invention) is the hypothesis that most scientific discoveries and inventions are made independently and more or less simultaneously by multiple scientists and inventors. The concept of multiple discovery opposes a traditional view—the "heroic theory" of invention and discovery. Multiple discovery is analogous to convergent evolution in biological evolution.