- published: 09 Nov 2014
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The permanent of a square matrix in linear algebra 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.
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 (2×2 matrix),
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. If one views the permanent as a map that takes n vectors as arguments, then it is a multilinear map and it is symmetric (meaning that any order of the vectors results in the same permanent). A formula similar to Laplace's for the development of a determinant along a row or column is also valid for the permanent; all signs have to be ignored for the permanent.
Geil or Geils may refer to:
A Christian ( pronunciation (help·info), (from the Ancient Greek: Χριστιανός Christianos) is a person who adheres to Christianity, an Abrahamic, monotheistic religion based on the life and teachings of Jesus of Nazareth as recorded in the Canonical gospels and the letters of the New Testament. "Christian" derives from the Koine Greek word Christ, a translation of the Biblical Hebrew term Messiah.
Central to the Christian faith is the gospel, the teaching that humans have hope for salvation through the message and work of Jesus, and particularly, his atoning death on the cross. Christians also believe Jesus is the Messiah prophesied in the Hebrew Bible. Most Christians believe in the doctrine of the Trinity ("tri-unity"), a description of God as Father, Son and Holy Spirit. This includes the vast majority of churches in Christianity, although a minority are Non-trinitarians.
The term "Christian" is also used adjectivally to describe anything associated with Christianity, or in a proverbial sense "all that is noble, and good, and Christ-like." It is also used as a label to identify people who associate with the cultural aspects of Christianity, irrespective of personal religious beliefs or practices.
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