The dimension of a given vector space is the number of elements of the basis.
If formula_1 is the vector space then:
formula_2 is a basis of formula_1.
It's easy to see that for any element of formula_1 it can be represented as a combination of the above basis.
Let formula_5 be any element of formula_1 and let formula_7.
Since formula_8 and formula_9 are elements of formula_10 then they can be written as formula_11 and so on.
Then the combination equals the element formula_5.
This shows that the set formula_13 is a basis of formula_1.
Prisoner of war
A prisoner of war (short form: POW) is a non-combatant who has been captured by the forces of the enemy, during an armed conflict. In past centuries, prisoners had no rights. They were usually killed or forced to be slaves. Nowadays prisoners of war have rights that are stated in the Geneva Conventions and other laws of war.
The Third Geneva Convention gives prisoners of war many different rights. Here are some examples:
If they are very sick or hurt, prisoners of war have the right to be let go. After a war ends, all prisoners must be let go quickly.
Prisoners of war also have the right NOT to:
Not all people who are caught while fighting wars are "prisoners of war." The Third Geneva Convention has a strict definition of what a prisoner of war is. For example, it says that to be "prisoners of war," soldiers must:
According to the Geneva Conventions, if soldiers do not meet these requirements, they are not "prisoners of war." They are "unlawful combatants" (which means "people who fight in ways that are against the law). This means they do NOT have the rights that are listed in the Geneva Conventions.
This caused controversy in the early 21st century. For example, in June 2002, the United States was fighting the War in Afghanistan. The Secretary of Defense, Donald Rumsfeld, announced that the people the U.S. had captured were "unlawful combatants [who] do not have any rights under the Geneva Convention[s]." The U.S. said these people were unlawful combatants, not prisoners of war, because:
The U.S. brought some of these people to a prison in Guantánamo Bay. Because they were enemy combatants, the inmates at Guantánamo did not get the rights that the Geneva Conventions give to prisoners of war.
When a country, or a group of people, does not give prisoners of war their rights, they are committing a war crime. However, punishing those war crimes has not always been easy.
The Geneva Convention lists the rights that prisoners of war have. However, there is nothing in the Geneva Convention that says how people should be punished when they do not give prisoners of war these rights.
In the past, when a country broke the Geneva Convention by not giving prisoners of war their rights, many different things might happen. For example, after World War II ended, the countries that won the war set up military tribunals called the Nuremberg Trials and the Tokyo Trials. At these trials, military leaders from Nazi Germany and the Empire of Japan were tried for crimes against prisoners of war (and many other things). Many of them were convicted and sentenced to death or to life in prison.
However, at other times, crimes against prisoners of war might be tried in the same country where the crimes happened. This might happen before or after the war ended. Sometimes crimes against prisoners of war were not punished at all.
In 2002, the International Criminal Court (ICC) was created to look into war crimes around the world, and punish people for them, if possible.
The ICC has a long list of crimes that are defined as war crimes. Some war crimes against prisoners of war are:
If a country, or a group of people, commit a war crime against prisoners of war, the ICC can put them on trial and punish them if they are found guilty.
Jackson's chameleon
Jackson's chameleon ("Trioceros jacksonii"), also known as the horned chameleon, Jackson's horned chameleon, or Kikuyu three-horned chameleon, is a species of chameleon found in the forests of Kenya and Tanzania. They have been introduced to the United States and Hawaii.
Males are easily recognized, they have two horns above their eyes and one horn on their nose. If males are kept together in a cage, they get stressed, and eventually die.
Females do not have horns, or if they do they are very small. Their biggest size is 15 inches. This species gives birth to live young with a gestation period of about 5-10 months.
Resuscitation
Resuscitation is a thing to do in a medical emergency. It is first aid which is given to a person who is unconscious, and where breathing or pulse can not be detected. It is done to make oxygen continues to reach the heart and the brain. That way, a doctor may be able to restart the heart, possibly without damaging the brain.
The most common cause for a stopping heart is a heart attack.
The person helping must:
Aubergine
The aubergine (also called eggplant) is a plant. Its fruit is eaten as a vegetable. The plant is in the nightshade family of plants. It is related to the potato and tomato. Originally it comes from India and Sri Lanka. The Latin/French term aubergine originally derives from the historical city of Vergina (Βεργίνα) in Greece. The aubergine eggplant is estimated to have reached Greek soils around 325 BC after the death of Alexander the Great in Babylon. Discovering this new vegetable during his conquest, Alexander the Great wished to bring it back to his country on his return. After his death, members of his army brought back seeds of the vegetable back to Greece and specifically to the city of Vergina (Βεργίνα). The Latin/French term aubergine (au·ber·gine) (\ˈō-bər-ˌzhēn\) is estimated around 1505 AD and is coined to Franco-Catalan gastronomist Sergius Rosario Silvestri, co-traveller and close friend to Amerigo Vespucci. Upon arrival to the historical site of Vergina (Βεργινα) and wanting to try the local delicacies, Silvestri came across the plant of aubergine. Not knowing its name, he referred to it as aubergine (au Bergine or au Vergine) which in French means "at Vergina" or "found at Vergina".
Coral Sea Islands
The Coral Sea Islands (or Coral Sea Islands Territory) is a group of islands on the Great Barrier Reef, in the country of Australia. Some islands have automatic weather stations or lighthouses on them. Willis Island is the only island where people live; four people there run a weather station. They are in the Coral Sea, northeast of Queensland.
Pernambuco
Pernambuco is a state of Brazil. The capital city of the state is Recife. About 8 million people live in Pernambuco with 1.5 million of those living in Recife. The economy is largely based on agriculture, its main exports are sugar cane and manioc. It has a mainly tropical climate.
Manioc
Manioc (or Cassava, or Yuca, especially in Latin America) is a shrub. It belongs to the Spurge family of plants and it grows in tropical climates. It is cultivated for its edible root. The manioc must be cooked properly to detoxify it before it is eaten and can be used in dumplings, soups, stews and gravies.
Life cycle
Life cycle means the stages a living thing goes through during its life.
In some cases the process is slow, and the changes are gradual. Humans have various stages of growth during their lives, such as zygote, embryo, child and adult. The change from a child to an adult is slow and continuous. In many societies it is marked by ceremonies at puberty.
In most insects the transition is sharp and well-defined: egg > larva > pupa > imago (adult).
In some animals, the parent generation looks different from the child. The most common case is that there are two different forms. One form will have sexual reproduction, the others might not reproduce, or might reproduce asexually.
Some plants and a few other organisms have a system called "alternation of generations" which is not quite the same because one form is haploid and the other is dipoid.