OpenLLM-France/wikimedia huggingface dataset:
# Defective matrix

In linear algebra, a defective matrix is a square matrix that does not have a complete basis of eigenvectors, and is therefore not diagonalizable. In particular, an $n\times n$ matrix is defective if and only if it does not have $n$ linearly independent eigenvectors. A complete basis is formed by augmenting the eigenvectors with generalized eigenvectors, which are necessary for solving defective systems of ordinary differential equations and other problems.
An $n\times n$ defective matrix always has fewer than $n$ distinct eigenvalues, since distinct eigenvalues always have linearly independent eigenvectors. In particular, a defective matrix has one or more eigenvalues $\lambda$ with algebraic multiplicity $m>1$ (that is, they are multiple roots of the characteristic polynomial), but fewer than $m$ linearly independent eigenvectors associated with $\lambda$. If the algebraic multiplicity of $\lambda$ exceeds its geometric multiplicity (that is, the number of linearly independent eigenvectors associated with $\lambda$), then $\lambda$ is said to be a defective eigenvalue. However, every eigenvalue with algebraic multiplicity $m$ always has $m$ linearly independent generalized eigenvectors.
A real symmetric matrix and more generally a Hermitian matrix, and a unitary matrix, is never defective; more generally, a normal matrix (which includes Hermitian and unitary matrices as special cases) is never defective.

## Jordan block

Any nontrivial Jordan block of size $2\times 2$ or larger (that is, not completely diagonal) is defective. (A diagonal matrix is a special case of the Jordan normal form with all trivial Jordan blocks of size $1\times 1$ and is not defective.) For example, the $n\times n$ Jordan block
    $J={\begin{bmatrix}\lambda &1&\;&\;\\\;&\lambda &\ddots &\;\\\;&\;&\ddots &1\\\;&\;&\;&\lambda \end{bmatrix}},$
has an eigenvalue, $\lambda$ with algebraic multiplicity $n$ (or greater if there are other Jordan blocks with the same eigenvalue), but only one distinct eigenvector $Jv_{1}=\lambda v_{1}$, where $v_{1}={\begin{bmatrix}1\\0\\\vdots \\0\end{bmatrix}}.$ The other canonical basis vectors $v_{2}={\begin{bmatrix}0\\1\\\vdots \\0\end{bmatrix}},~\ldots ,~v_{n}={\begin{bmatrix}0\\0\\\vdots \\1\end{bmatrix}}$ form a chain of generalized eigenvectors such that $Jv_{k}=\lambda v_{k}+v_{k-1}$ for $k=2,\ldots ,n$.
Any defective matrix has a nontrivial Jordan normal form, which is as close as one can come to diagonalization of such a matrix.

## Example

A simple example of a defective matrix is
    ${\begin{bmatrix}3&1\\0&3\end{bmatrix}},$
which has a double eigenvalue of 3 but only one distinct eigenvector
    ${\begin{bmatrix}1\\0\end{bmatrix}}$
(and constant multiples thereof).
# Hobie Tiger

The Hobie Tiger or Hobie Tiger 18, is a French catamaran sailboat that was designed by Hobie Cat Europe as a Formula 18 racer and first built in 1995.
The boat is an International Sailing Federation recognized international class.

## Production

The design was built by Hobie Cat Europe in France, starting in 1995 and later by the parent company Hobie Cat in the United States in 2001, but it is now out of production.

## Design

The Hobie Tiger is a sailing dinghy, with the twin hulls built predominantly of polyester fiberglass sandwich with a foam core.
The hulls have plumb stems and transoms, transom-hung rudders controlled by a single tiller and twin retractable daggerboards. It has a fractional sloop rig with aluminum spars, including a rotating mast, stepped on the fore beam. The rigging is wire. It displaces 397 lb (180 kg) and is normally sailed by a crew of two sailors, both of whom are provided with trapezes to balance the boat.
The boat has a draft of 2.33 ft (0.71 m) with a daggerboard extended and 3.00 in (7.6 cm) with both retracted, allowing operation in shallow water, beaching or ground transportation on a trailer.
For sailing downwind the design may be equipped with an asymmetrical spinnaker of 226 sq ft (21.0 m$^2$).
The design has a Portsmouth Yardstick RYA PN handicap number of 693.
# TAC4

Tachykinin-4 is a protein that in humans is encoded by the TAC4 gene.
This gene is a member of the tachykinin family of neurotransmitter-encoding genes. Tachykinin proteins are cleaved into small, secreted peptides that activate members of a family of receptor proteins. The products of this gene preferentially activate tachykinin receptor 1 and are thought to regulate peripheral endocrine and paracrine functions including blood pressure, the immune system, and endocrine gland secretion. The products of this gene lack a dibasic cleavage site found in other tachykinin proteins. Consequently, the nature of the cleavage products generated in vivo remains to be determined. Multiple transcript variants encoding different isoforms have been found for this gene.
# Hormuz-class vessel

Two ship classes of the Navy of the Islamic Revolutionary Guard Corps have been named Hormuz:
* Hormuz 21 class
* Hormuz 24 class
# Sundays River Valley

The Sundays River Valley is a low-lying area along the Sundays River. It forms part of the Sunday's River Valley Local Municipality in Sarah Baartman District Municipality, Eastern Cape, South Africa.
The valley stretches from the Kirkwood prison grounds in the west to Colchester and Kinkelbos in the southeast. It is characterized by high-intensity agricultural activities (in particular the production of citrus fruits) and a well-developed irrigation system. In addition to citrus cultivation, various tourist attractions, bed and breakfast facilities, packing sheds and game-related tourist facilities are present throughout the valley.
The main urban settlement in the valley is Kirkwood. It also contains Enon, Colchester, Bersheba and Addo. Smaller settlements include Sunlands and Kinkelbos.
The Sundays River Valley irrigation scheme was started in the early 1920s, targeting British settlers on small holdings (10 morgen in size) along the banks of the Sundays River. A large dam was constructed on the Sundays River (Lake Mentz) to supply the area with water for irrigation, and a canal system was put in place to supply water to farms from Kirkwood, at the upper end of the valley, to Addo at the lower end. The driving force of this development was Sir Percy Fitzpatrick.$^{:14}$
This area is now one of the key production areas for citrus in South Africa.$^{:14}$
# The Cadets

The Cadets can refer to one of the following:
* The Cadets Drum and Bugle Corps
* The Cadets (group), an American doo-wop group
* The Cadets (TV series) - 10-part Russian TV series dealing with the Battle of Stalingrad
# Cornufer manus

Cornufer manus is a species of frog in the family Ceratobatrachidae. It is endemic to the Nakanai Mountains on New Britain Island in Papua New Guinea.

## Original publication

* Fred Kraus; Allen Allison (2009). "New species of frogs from Papua New Guinea". Bishop Museum Occasional Papers (Abstract and figures). 104: 1–36. Retrieved February 2, 2023.
# Sunland Park

Sunland Park may refer to:
* Sunland Park, New Mexico
* Sunland Park Racetrack & Casino, in Sunland Park, New Mexico
* Sunland Park Mall, in El Paso, Texas
* Sunland Park, in Sunland, California
# Arpa jarocha

The arpa jarocha is a large wooden harp that is normally played while standing, although early examples from the 16th through the first three or four decades of the 19th centuries were smaller and were played while seated. It has a wooden frame, a resonator, a flat soundboard, 32-36 nylon strings (originally, gut strings), and does not have pedals. This harp is tuned diatonically over five octaves. The top of its soundboard sometimes arches outward due to the tension of the strings. Unlike other Mexican harps, the arpa jarocha has its sound holes located on the back of the soundboard instead of on the front.

## Playing technique

As previously stated, the arpa jarocha was once commonly played while seated, similarly to its ancestor the Spanish harp from the 16th century. In modern times, since approximately the 1940s, the arpa jarocha has been built in a larger scale, following the general pattern of the Western Mexican harps from Jalisco and Michoacán. One of the first recording artists of the genre, Andrés Huesca (1917-1957), actually used a Michoacán harp, due to its better volume for recording. The performer uses one hand to play the bass line on the low strings, and uses the other hand to play arpeggiated melodies on the higher strings. The soundboard has also been known to be used as a percussive device, though this is rare. That practice is common in the Tierra Caliente groups of Michoacan, however.

## Use

The arpa is one of the main instruments used in the conjunto jarocho; a type of Mexican folk ensemble. The musical style in which arpa jarocha is also heard is "sones jarochos," which blends Spanish and African-influenced rhythms. Within this genre, the arpa typically provides the main melodies, while instruments such as the jarana guitar and the requinto provide rhythms and counter-melodies.
Both men and women play this instrument, although a greater percentage are men.

## Origins

The arpa jarocha is from Veracruz, Mexico. one of the various forms of harp that evolved from models introduced by Spain in the 16th century, and traced even back further to the Arabs who had occupied Spain for 700 years.
The indigenous people of Veracruz had never seen stringed instruments before the Conquest, and quickly adapted their own version which became a pivotal instrument used in many different musical ensembles in Veracruz, but also the rest of Mexico and Latin America.

## Misconceptions

Some references have stated that the arpa jarocha was used in Jalisco, Michoacán, and among the Chamula Indians; this is incorrect. Each of those regions developed their own adaptation of the baroque Spanish harp. Also, there were regional harps in Zacatecas and in the North with the Yaqui Indians of the northern desert and southwest US.

## Similar instruments

There are multiple variations of the arpa, depending on where it comes from. The arpa llanera, arpa aragüeña, and arpa criolla originate from Venezuela, the arpa indígena originates from Peru, and the arpa paraguaya originates from Paraguay.
# Aspelta (rotifer)

Aspelta is a genus of rotifers within the family Dicranophoridae. Members of this genus can be found in multiple areas throughout the world.

## Species

* Aspelta clydona Harring & Myers, 1928
* Aspelta europaea Hauer, 1939
* Aspelta harringi Remane, 1929
* Aspelta lestes Harring & Myers, 1928
* Aspelta pachida (Gosse, 1887)
* Aspelta reibischi (Remane, 1929)
# Thaba Mokhele

Thaba Mokhele is a community council located in the Mohale's Hoek District of Lesotho. Its population in 2006 was 18,135.

## Villages

The community of Thaba-Mokhele includes the villages of:
* Boikhutsong
* Five Rand
* Ha 'Mako
* Ha Belemane
* Ha Biane
* Ha Bokoro
* Ha Chefa
* Ha Faetoa
* Ha Jimi
* Ha Kaphe (Maholong)
* Ha Kaphe (Moreneng)
* Ha Khanyane
* Ha Khoale
* Ha Kholoane
* Ha Kooko
* Ha Lisene
* Ha Mabaka
* Ha Mahlelebe
* Ha Mahooana (Mahahaneng)
* Ha Mako (Ha Folatsane)
* Ha Mako (Mahlalela)
* Ha Mapuru
* Ha Maqeba
* Ha Maqoala
* Ha Masita
* Ha Matseo
* Ha Moeletsi
* Ha Mohale
* Ha Mokhothu
* Ha Mokunyane
* Ha Moloche
* Ha Monakalali
* Ha Moshabe
* Ha Mosika
* Ha Mosotho
* Ha Mothe
* Ha Mothetho
* Ha Ntepe
* Ha Ntsapi
* Ha Pekenene
* Ha Phala
* Ha Pitseng
* Ha Qoane
* Ha Rakhenku
* Ha Ralepei
* Ha Ramahloli
* Ha Ramahlolonyane
* Ha Ramatlali
* Ha Ramokongoane
* Ha Rampeli
* Ha Rantšoeu
* Ha Ranyakane
* Ha Rasebolelo
* Ha Rathobeli
* Ha Ratšoeu
* Ha Seabata
* Ha Sehloho
* Ha Sekunyane
* Ha Sepinare (Moreneng)
* Ha Sepinare (Sekiring)
* Ha Soere
* Ha Taele
* Ha Tepa
* Ha Thetela
* Ha Thokoa
* Ha Tšese
* Hloahloeng
* Hohobeng
* Kalakeng
* Khang-ka-Khotso
* Kholokoe
* Kolobere
* Kopialena
* Lefikeng
* Lefikeng (Thaba-Tšoeu)
* Lekhalong
* Letlapeng
* Lifateng (Ha Nkunyane)
* Lifateng (Lekhalong)
* Lifateng (Moreneng)
* Lifateng (Motse-Mocha)
* Lifateng (Thoteng)
* Lifateng (Tšoeneng)
* Linokong
* Liphofung (Ha Ralijeng)
* Lithabaneng (Boithatelo)
* Lithakaling
* Maboneng
* Makhaloaneng
* Makutoaneng
* Maqoala
* Matsatseng
* Matsaung
* Matsekeng
* Matsoapong
* Motsekong
* Nk'hunk'hu
* Nkoboto
* Noka-Ntšo
* Nomoroane
* Ntširele
* Patisa
* Phahameng
* Phohlokong
* Pontšeng
* Sehlabaneng
* Senekane
* Terai Hoek (Ha Molomo)
* Thabana- Ntšonyana
* Thabaneng-tsa-Marole
* Thoteng and Tutululung
# Daniel Glaser

Daniel L. Glaser is a former Assistant Secretary for Terrorist Financing at the United States Department of the Treasury. He served under Adam Szubin, the Under Secretary of the Treasury for Terrorism and Financial Intelligence in the Obama Administration. His work came into prominence as the result of a 2010 WikiLeaks document dump.
Glaser received a B.A. from the University of Michigan and a J.D. from Columbia Law School. Previously, he worked at Coudert Brothers and held various positions in the George W. Bush administration.
# List of King George V Playing Fields in Derbyshire

Derbyshire :
| Location | Formal name | Local name (if any) | National Grid Reference | Dates | Dates | External links |
| Location | Formal name | Local name (if any) | National Grid Reference | Purchase | Opening | External links |
| Oddfellows Road Hathersage | King George V Field | Swimming Pool/Playing Field/Bowling Green | SK232813 | 1935/36 | | |
# The Cookie Jar Foundation

The Cookie Jar Foundation is a non-profit foundation established to help meet funding requirements for beneficiaries including the Edinburgh Sick Kids Hospital, the young persons group at Maggies Cancer Centre at the Western General Hospital and the cancer units at the Victoria Hospital, Kirkcaldy. The charity is named after Christopher "Cookie" Coutts who died after a valiant fight with Hodgkin's Lymphoma aged 19.

## Events
### Dunfermline Press and Central Fife Times Charity of the Year 2015

Nominated by employees at the Victoria Hospital in Kirkcaldy who used the vein-finder technology donated by the charity, the foundation was given this award for their numerous fundraising efforts and came within 18 months of their official charity status. At this point they had raised £33,000 in total and were awarded a further £400 as a result of their award.

### Leon Rendle

The foundation got involved when hearing that Leon, battling a rare form of incurable cancer, was rejected insurance for one of his final wishes to fly to Orlando for a holiday with his family. The Cookie Jar assisted by seeking out alternative methods of getting the insurance from the United States in order to secure the family's holiday together.

### The Long Road To Home 2014/London Marathon 2015 - Tom Main

Tom Main, a good friend of Christopher and his family, ran four marathons in four days from his University in Aberdeen to Christopher's home in Aberdour, Fife. His run accumulated 120 miles and raised a total of £3,000 for the foundation. A year later Tom ran the London Marathon without intense training to represent the fight that Christopher gave towards his illness. His efforts raised a further £1,400 for the charity.

### The 5 Ferries Sponsored Cycle 2015

The 5 Ferry Challenge was organised by the Edinburgh law firm MacLay, Murray and Spens (MMS) and took place on Saturday 30 May with a mixed group of 25 participants from MMS family and friends and cyclists. This event and numerous others organised by the firm raised £20,000 and the Cookie Jar remains as one of the firm's main supported charities.
# Cornufer heffernani

Cornufer heffernani, sometimes known as the Solomon Island palm frog, is a species of frog in the family Ceratobatrachidae. It is endemic to the Solomon Islands archipelago where it can be found in at least Buka and Bougainville Islands of Papua New Guinea and Choiseul and Santa Isabel Islands of the Solomon Islands, but probably also more widely. The specific name heffernani honours Mr. N. S. Heffernan, who collected the type series.

## Taxonomy

Cornufer heffernani was until 2015 known as Palmatorappia solomonis, the sole species of the genus Palmatorappia. In a major revision of family Ceratobatrachidae, Brown and colleagues moved P. solomonis to the genus Cornufer, leading to secondary homonymy with Cornufer solomonis. They solved this issue by resurrecting Cornufer heffernani as a substitute name. Palmatorappia could still be recognized as a monotypic subgenus Cornufer (Palmatorappia).

## Description

Cornufer heffernani has a small, delicate, slender body and limbs. A syntype specimen of Hylella solomonis in the Senckenberg Museum measures 28 mm (1.1 in) in snout–vent length. The head is broader than the body and triangular in shape. The snout is broadly rounded and the eyes are large. The canthus rostralis and the tympanum are indistinct. The limbs are slender. Both the fingers and the toes are webbed and bear well-developed discs. Skin is smooth above but granular on the flanks, the belly, and under surface of the upper arm and thighs. Preserved specimens are purplish brown above and yellow below, fading to yellowish all over with time.

## Habitat and conservation

Cornufer heffernani is a very rare species that is found on low vegetation and trees in tropical rain forests. It can also be found in good-quality secondary forests. It has direct development, that is, it breeds without free-living tadpole stage. It is threatened by habitat loss caused by logging.
# Summerfield Research Station

The Summerfield Research Station is a development and production site for solid rocket motors in the United Kingdom officially formed on 1 September 1951 by the Ministry of Supply. It was set up on the grounds of a former World War II munitions factory just south of Kidderminster, southwest of Birmingham. It opened on 1 January 1952 and remains in use as of 2020.
Previous UK rocket motors, like those on the RP-3, used Cordite as their propellant, formed into a solid using various binders and then moulded into cylinders with internal cavities to control the rate of burn. While the US adopted the UK concept of shaped cavities, the UK adopted the US double-base powder, which was the basis for contemporary US rocket designs and offered higher energy. The combination of these two features formed the basis for military rockets until the introduction of aluminum-boosted propellants in the 1960s.
Since its formation, the site has produced rocket motors for many UK weapons systems. Among its early successes was a motor design for the Sea Slug missile, which allowed that design to switch from a liquid fuel rocket, considered a hazard on ships. Other successes include the motors for Vigilant, Swingfire, MILAN, Thunderbird, Seacat, Sea Dart, Sea Wolf and Sea Skua. Over the years, solid rocket design was centralized at Summerfield, taking on employees from the Rocket Propulsion Establishment and the Propellants, Explosives and Rocket Motor Establishment at the Waltham Abbey Royal Gunpowder Mills as those establishments closed.
Summerfield was initially run by Imperial Chemical Industries, but in 1975 it was handed off to their subsidiary, Imperial Metal Industries (IMI) to become IMI Summerfield. The division was purchased by British Aerospace in 1998 and over the next few years changed name several times until BAe merged the division with the French firm Celerg to form Roxel. Today the site is officially known as Roxel (UK Rocket Motors) Limited.
# Talmadge Prince

Talmadge "Tab" Prince (February 16, 1938 – February 19, 1970) was an American stock car racing driver.

## Early life

Talmadge Prince was born February 16, 1938, in Cullman, Alabama. He was the fourth of six children born to William Taft Prince and Marie Cryer Prince. In 1969 he bought a 50% share of a Chrysler/Plymouth dealership in Dublin, Georgia. He financed the purchase using the proceeds from the sale of his business, PBR Electronics, to his older brother, William Lloyd Prince.
Talmadge was married twice. In 1959 he married Jeanette Ellen Looney. They had two children. He married his second wife, Nell Sutton, in 1969. They had one son who was born after his death.

## Racing career

Prince started racing cars in the early 1960s, racing sprint and Late Model Sportsman cars on short tracks in the American South. In 1970, he entered his first NASCAR Grand National Series event, the Daytona 500. Prince's career only lasted a very unfortunate 18 laps.

## Fatal accident

In the second of the two 125 mile qualifying races for the Daytona 500 he blew an engine on his Dodge Daytona and went into a slide. Bill Seifert, who was following behind Prince, got into oil, lost control, and broadsided onto the driver's side of Prince's car. Prince was killed instantly. He was buried at the Roselawn Cemetery in Decatur, Alabama, and was survived by two sons and a daughter. His crash was similar to Harold Kite's fatal crash in 1965.

## Motorsports career results
### NASCAR

(key) (Bold - Pole position awarded by qualifying time. Italics - Pole position earned by points standings or practice time. * – Most laps led.)

#### Grand National Series

NASCAR Grand National Series results :
| Year | Team | No. | Make | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | NGNC | Pts |
| 1970 | Talmadge Prince | 78 | Dodge | RSD | DAY | DAY 28 | DAY DNQ | RCH | CAR | SVH | ATL | BRI | TAL | NWS | CLB | DAR | BLV | LGY | CLT | SMR | MAR | MCH | RSD | HCY | KPT | GPS | DAY | AST | TPN | TRN | BRI | SMR | NSV | ATL | CLB | ONA | MCH | TAL | BGS | SBO | DAR | HCY | RCH | DOV | NCF | NWS | CLT | MAR | MGR | CAR | LGY | NA | 0 |
# Vlassov

Vlassov is a surname. Notable people with the surname include:
* Alexander Vlassov (born 1955), Soviet pair skater
* Julia Vlassov (born 1990), American pair skater
* Jüri Vlassov (1948), Estonian actor and singer
* Viktor Vlassov (born 1951), Soviet sport shooter
# Diane Lindsay

Captain Diane M. Lindsay was the first black woman to be awarded the Soldier's Medal.
In 1969 Diane M. Lindsay volunteered with the US Army Nurse Corps as a First Lieutenant at the 95th Evacuation Hospital in Vietnam, where she convinced a confused US soldier to surrender a grenade, which he had pulled the pin of and was preparing to throw within the hospital. Lindsay's actions saved the lives of numerous people and earned her the Soldier’s Medal. She was the first black woman to receive the award. Lindsay was eventually promoted to captain.
# TINAG

Tubulointerstitial nephritis antigen is a protein that in humans is encoded by the TINAG gene.
TINAG is a basement membrane glycoprotein initially identified as a target of antibodies in some forms of immunologically mediated tubulointerstitial nephritis.[supplied by OMIM]
# Annów, Tomaszów Mazowiecki County

Annów is a village in the administrative district of Gmina Czerniewice, within Tomaszów Mazowiecki County, Łódź Voivodeship, in central Poland. The population is 187. It lies approximately 3 kilometres (2 mi) south-east of Czerniewice, 19 km (12 mi) north-east of Tomaszów Mazowiecki, and 53 km (33 mi) east of the regional capital Łódź.
# Director Musices

Director Musices is computer software produced by the Department of Speech, Music and Hearing at KTH Royal Institute of Technology. It aims to give an expressive, human-like performance to a musical score by varying the volume and timing of the notes. Director Musices is written in CMU Common Lisp and distributed as free software. It processes MIDI files.