Linear independence is a concept from linear algebra. It is used to talk about vector spaces. Each vector space has a null vector. This vector is expressed as a linear combination (a sum) of other vectors. A set of these vectors is called "linearly independent" if and only if all of them are needed to express this null vector. This is equivalent to saying that at least one of the vectors can be expressed as a linear combination of the others. If the vectors are not linearly independent, they are called "linearly dependent".
As an example, take the three-dimensional Euclidean space:
Here the first three vectors are linearly independent; but the fourth vector equals nine times the first plus five times the second plus four times the third, so the four vectors together are linearly dependent. Linear dependence is a property of the family, not of any particular vector; for example in this case we could just as well write the first vector as a linear combination of the last three.
Division of Blair
The Division of Blair is an Australian Electoral Division in Queensland. Created in 1998, it is named after Harold Blair, an Aboriginal singer and civil rights campaigner. It covers an area of 6,409 km² west of Brisbane and includes Kilcoy, Toogoolawah, Esk, Cominya, Lowood, Fernvale, Ipswich, Minden, Marburg, Rosewood, and Walloon.
During the 2007 election campaign Blair received more funding promises from the Howard Government than any other electorate in the country.
Mary Kom
Mangte Chungneijang Mary Kom (b. 1 March 1983) is an Indian boxer. Kom is a member of the Kom tribe of north-east India. She was born in Kangathei, Churachandpur, Manipur.
Since childhood, Kom has liked athletics boxing and was good at them. She became interested in boxing after watching Dingko Singh in 2000. That same year, she began training with M. Narjit Singh (Manipur State Boxing Coach) at Khuman Lampak, Imphal.
Kom has won the World Boxing championship five times in a row. She is the only woman to get a medal and trophy in all six world championships. She is also the only Indian woman to qualify for boxing in the 2012 London Olympics. At the 2013 Games, she competed in the flyweight category 51kg and won a bronze medal. She had also been ranked as No. 1 AIBA World Women's Ranking Light Flyweight category.
Kom is married to K Onler Kom. They have twin sons named Rechungvar and Khupneivar. She lives with her family in Manipur.
Count of Anjou
Count of Anjou was a title first given to Ingelger. His male line ended with Geoffrey II of Anjou. The next line of counts of Anjou were descended from Geoffrey's sister Ermengarde-Blanche and her husband Geoffrey II, Count of Gâtinais. Their descendants include the Plantagenet kings of England.
In 1204, Anjou was lost to king Philip II of France. It was re-granted as an appanage for Louis VIII's son John. He died in 1232 at the age of thirteen. Anjou was then given to Louis's youngest son, Charles. He later became the king of Sicily.
In 1290, Margaret married Charles of Valois, the younger brother of king Philip IV of France. He became Count of Anjou in her right.
Ingelger
Ingelger (or Ingelgarius) († ) was a Frankish nobleman who became the first count of Anjou. He began a known as House of Ingelger.
Ingelger was the son of a Frankish nobleman Tertullus and his wife Petronilla. She was the niece of Raino, Bishop of Angers. Petronilla was also a relative of Hugh the Abbot, an counselor to both Louis II and Louis III of France. His mother's influence was one of the reasons for Ingelger's success. Records of the time call Ingelger a "miles optimus" (a great military man). Louis II appointed Ingelger as viscount of Orléans which at the time was under the rule of the Bishop of Orléans. While at Orléans Ingelger married Adelais. Later Ingelger was appointed prefect (military commander) at Tours. Some time after this Ingelger was made Count of Anjou. At this time the county went only as far west as the Mayenne River. He was buried in the church of Saint-Martin at Châteauneuf-sur-Sarthe.
Ingelger married Adelis, a close relative of Raino, Bishop of Angers. He was succeeded by their son:
Tyndall effect
The Tyndall effect is when light is scattered by particles of matter in its path. It makes a beam of light visible by lighting the particles.
Under the Tyndall effect, the longer-wavelength light is more transmitted while the shorter-wavelength light is more reflected by scattering. In effect, blue light is scattered much more strongly than red light.
The blue of a clear sky, and the blue of blue eyes is caused by the Tyndall effect, not by a pigment. Its named after John Tyndall.
Tyndall effect can also be observed when sunlight passes through the canopy of a dense forest.
It happens due to the scattering of light by the particles of smoke and dust.
Bandai-Azuma Roadway
Mid-Sea Road
Mid-Sea Road is a road in Uruma, Okinawa in Japan. It connects two islands.
Arrondissements of the Pyrénées-Orientales department
There are 3 arrondissements in the Pyrénées-Orientales department. The French departments, and in other countries, are divided into "arrondissements", which may be translated into English as districts (in some cases, as boroughs). The capital of an arrondissement is called a subprefecture.
If the prefecture (capital) of the department is in an arrondissement, that prefecture is the capital of the arrondissement, acting both as a prefecture and as a subprefecture. Arrondissements are further divided into communes.
The arrondissements of Pyrénées-Orientales are:
Since its creation, the Pyrénées-Orientales department, first with the name of Roussillon, has had few changes:
Arrondissement of Céret
The arrondissement of Céret is an arrondissement of France; it is the southermost "arrondissement" of Metropolitan France. It is part of the Pyrénées-Orientales "département". Its capital is the city of Céret.
The "arrondissement" of Céret is in the southeast of the department; it is the southernmost "arrondissement" of France.
When the Pyrénées-Orientales department was created on 17 February 1800, the "arrondissement" of Céret was part of that original department.
The "arrondissement" of Céret is the smallest of the "arrondissements" of the department, with an area of , but it is the second in population, after the Perpignan "arrondissement", with 73,192 inhabitants and a density of inhabitants/km².
The "arrondissement" is bordered to the north by the Perpignan "arrondissement", to the east by the Mediterranean Sea, to the south by Spain, to the west and northwest by the Prades "arrondissement".
After the reorganisation of the cantons in France, cantons are not subdivisions of the "arrondissements" so they could have "communes" that belong to different "arrondissements".
In the "arrondissement" of Céret, there are 2 cantons whose "communes" are in the "arrondissement": La Côte Vermeille and Vallespir-Albères. The following table shows the distribution of the "communes" in the cantons and "arrondissements":
The "arrondissement" of Céret has 40 "communes"; they are (with their INSEE codes):
The "communes" with more inhabitants in the "arrondissement" are:
Arrondissement of Perpignan
The arrondissement of Perpignan is an arrondissement of France. It is part of the Pyrénées-Orientales "département". Its capital is the city of Perpignan.
When the Pyrénées-Orientales department was created on 17 February 1800, the "arrondissement" of Perpignan was part of that original department.
The arrondissement of Perpignan is in the northeast of the department; it is the second in area, after Prades, of the "arrondissements" of the department, with an area of , but it is the first in population with 349,959 inhabitants and a density of inhabitants/km².
The "arrondissement" is bordered to the north by the Aude department, to the east by the Mediterranean Sea, to the south by the Céret "arrondissement" and to the west by the Prades "arrondissement".