Unitary group

In mathematics, the unitary group of degree n, denoted U(n), is the group of n × n unitary matrices, with the group operation that of matrix multiplication. The unitary group is a subgroup of the general linear group GL(n, C). Hyperorthogonal group is an archaic name for the unitary group, especially over finite fields.

In the simple case n = 1, the group U(1) corresponds to the circle group, consisting of all complex numbers with absolute value 1 under multiplication. All the unitary groups contain copies of this group.

The unitary group U(n) is a real Lie group of dimension n². The Lie algebra of U(n) consists of n × n skew-Hermitian matrices, with the Lie bracket given by the commutator.

The general unitary group (also called the group of unitary similitudes) consists of all matrices A such that A^∗A is a nonzero multiple of the identity matrix, and is just the product of the unitary group with the group of all positive multiples of the identity matrix.

Properties

Since the determinant of a unitary matrix is a complex number with norm , the determinant gives a group homomorphism

United Nations

The United Nations (UN) is an intergovernmental organization to promote international co-operation. A replacement for the ineffective League of Nations, the organization was established on 24 October 1945 after World War II in order to prevent another such conflict. At its founding, the UN had 51 member states; there are now 193. The headquarters of the United Nations is in Manhattan, New York City, and experiences extraterritoriality. Further main offices are situated in Geneva, Nairobi and Vienna. The organization is financed by assessed and voluntary contributions from its member states. Its objectives include maintaining international peace and security, promoting human rights, fostering social and economic development, protecting the environment, and providing humanitarian aid in cases of famine, natural disaster, and armed conflict.

During the Second World War, US President Franklin D. Roosevelt initiated talks on a successor agency to the League of Nations, and the United Nations Charter was drafted at a conference in April–June 1945; this charter took effect 24 October 1945, and the UN began operation. The UN's mission to preserve world peace was complicated in its early decades by the Cold War between the US and Soviet Union and their respective allies. The organization participated in major actions in Korea and the Congo, as well as approving the creation of the state of Israel in 1947. The organization's membership grew significantly following widespread decolonization in the 1960s, and by the 1970s its budget for economic and social development programmes far outstripped its spending on peacekeeping. After the end of the Cold War, the UN took on major military and peacekeeping missions across the world with varying degrees of success.

U.N. (group)

U.N. is a Harlem-based hip hop group founded by Cam'ron in 2009. The group came to formation after Cam'ron had a falling-out with fellow Harlem rapper and co-founder of The Diplomats Jim Jones in 2007.

Currently

Cam'ron, Vado, and DJ Drama released a mixtape entitled, "Boss of All Bosses," on August 12, 2009 followed by a second mixtape called, "Boss of All Bosses 2," on January 12, 2010. Both mixtapes were released under The U.N. banner. Additionally, The U.N. released Boss of All Bosses 2.5, an expansion of the first two original mixtapes, released on May 12, 2010. Cam'ron and Vado have since announced future plans for a solo Vado mixtape and album, as well as a U.N. album distributed by Asylum.

Cam'ron and Vado have released their first official U.N. album entitled Cam'ron & The U.N. Presents: "Heat in Here" Vol. 1 on May 25, 2010, manufactured and distributed by Asylum Records. Guest appearances on the album include rappers: Young Chris, Gucci Mane, and Felony Fame.

Additionally, The U.N. released the long awaited "Gunz N' Butta" album on April 19, 2011 through "Diplomatic Man Inc." and E1 Music. It features the singles: "Speakin' in Tungs" and "Hey Muma."