Permanent
In linear algebra, the permanent of a square matrix is a function of the matrix similar to the determinant. The permanent, as well as the determinant, is a polynomial in the entries of the matrix. Both permanent and determinant are special cases of a more general function of a matrix called the immanant.
Definition
The permanent of an n-by-n matrix A = (ai,j) is defined as
The sum here extends over all elements σ of the symmetric group Sn; i.e. over all permutations of the numbers 1, 2, ..., n.
For example,
and
The definition of the permanent of A differs from that of the determinant of A in that the signatures of the permutations are not taken into account.
The permanent of a matrix A is denoted per A, perm A, or Per A, sometimes with parentheses around the argument. In his monograph, Minc (1984) uses Per(A) for the permanent of rectangular matrices, and uses per(A) when A is a square matrix. Muir (1882) uses the notation 
.
The word, permanent, originated with Cauchy in 1812 as “fonctions symétriques permanentes” for a related type of function, and was used by Muir (1882) in the modern, more specific, sense.
Permanent (song)
"'Permanent" is a song recorded by American rock singer David Cook. Written by Cook, Chantal Kreviazuk, and Raine Maida, its lyrics make allusions to Cook's late brother, Adam, who had battled with brain cancer before his death from this disease. The song was performed on the finale of season 8 of the TV show American Idol, and the performance then released onto iTunes as a charity single via RCA Records on May 18, 2009. It also appears on his debut studio album, David Cook (2008).
All proceeds from iTunes sales of the American Idol finale performance of the song will go to ABC2 (Accelerate Brain Cancer Cure).
Commercial reception
"Permanent" debuted at number 24 on the U.S. Billboard Hot 100 chart for the chart week of May 29, 2009, and number 10 on the Digital Songs component chart, selling 103,000 downloads. It also debuted at number 26 on the Billboard Canadian Hot 100 and number 7 on the Canadian Digital Songs component chart. As of June 2009, the song has sold 159,000 units, of which 98,000 are of the version on David Cook and 61,000 are from the AI Charity Version.
Permanent (disambiguation)
Permanent is a concept in linear algebra.
Permanent may also refer to:
Art, entertainment, and media
Music
Albums
Songs
Other uses
See also
Jana Kramer
Jana Rae Kramer (born December 2, 1983) is an American actress and country music singer. She is best known for her role as Alex Dupre on the television series One Tree Hill. Kramer began a country music career in 2012 with the single "Why Ya Wanna" from her self-titled debut album for Elektra Records.
Early life
Kramer was born in Rochester Hills, Michigan, United States, to Nora and Martin Kramer. She is of German Chilean, Croatian and French ancestry. Jana has one brother Steve who is a police officer. Jana attended Rochester Adams High School. She speaks some German.
Career
2002–11: acting career and record deal
In 2002, Kramer made her acting debut in the low-budget independent horror film Dead/Undead. The following year Kramer guest appeared on All My Children, which marked Kramer's television debut. Kramer has since continued to appear in a number of television shows such as CSI: Crime Scene Investigation, Grey's Anatomy, Private Practice and CSI: NY. She has also had small supporting roles in films such as Click, Prom Night and Spring Breakdown.
Love (Cirque du Soleil)
Love is a 2006 theatrical production by Cirque du Soleil which combines the re-produced and re-imagined music of the Beatles with an interpretive, circus-based artistic and athletic stage performance. The show plays at a specially built theatre at the Mirage in Las Vegas.
A joint venture between Cirque and the Beatles' Apple Corps Ltd, it is the first theatrical production that Apple Corps Ltd. has partnered in. Love is written and directed by Dominic Champagne. Music directors are Sir George Martin, producer of nearly all of the Beatles' records, and his son, record producer Giles Martin. A soundtrack album of the show was released in November 2006.
History
The project arose from discussions in 2000 between George Harrison and his friend Guy Laliberté, one of Cirque's founders. Three years of negotiations between surviving members of the Beatles, Sir Paul McCartney and Ringo Starr, The Beatles widows Olivia Harrison (representing George Harrison) and Yoko Ono (representing John Lennon), the Beatles' holding company Apple Corps Ltd. and the MGM Mirage culminated in an agreement.
Love (Angels & Airwaves album)
Love is the third studio album by alternative rock band Angels & Airwaves. It was released on February 12, 2010 on Fuel TV, and on February 14 on Modlife. The album was released free of charge due to "corporate underwriting". A "special edition" hard copy version of the album was scheduled for release on March 22, 2011, along with a second disc containing new music from the band. This was announced at a Q & A for the movie, which stated that it would be pushed back to Fall of 2011.
Production
On January 12, 2010, the band released a promotional video entitled "C:\Transmission_Love", which contained a short preview of The Flight of Apollo.
Release and special editions
In May 2009, it was announced that the album would be released on Christmas Day. However, on July 19, 2009, DeLonge announced via Modlife that the album will not be released on Christmas Day as previously planned, and instead will be released on Valentine's Day. The album was released free of charge through Modlife on Valentine's Day 2010.
Podcasts:
