Editing Matrix representation (section)

{{About|the layout of matrices in the memory of computers|the representation of [[group (mathematics)|groups]] and [[algebra over a field|algebras]] by matrices in linear algebra|representation theory}}
[[File:Row_and_column_major_order.svg|thumb|upright|Illustration of [[row- and column-major order]] ]]
'''Matrix representation''' is a method used by a [[computer language]] to store column-vector [[matrix (mathematics)|matrices]] of more than one dimension in [[computer storage|memory]].
[[Fortran]] and [[C (programming language)|C]] use different schemes for their native arrays. [[Fortran]] uses "Column Major", in which all the elements for a given column are stored contiguously in memory. [[C (programming language)|C]] uses "Row Major", which stores all the elements for a given row contiguously in memory.
[[LAPACK]] defines various matrix representations in memory. There is also [[Sparse matrix representation]]  and [[Morton-order matrix representation]].
According to the documentation, in [[LAPACK]] the [[unitary matrix]] representation is optimized.<ref name=utexas>{{cite web|title=Representation of Orthogonal or Unitary Matrices|url=http://www.ma.utexas.edu/documentation/lapack/node117.html|publisher=University of Texas at Austin|accessdate=14 September 2011}}</ref><ref>{{cite journal |first=R. |last=Lehoucq |title=The Computation of Elementary Unitary Matrices |journal=ACM Transactions on Mathematical Software |volume=22 |issue=4 |year=1996 |pages=393–400 |doi=10.1145/235815.235817 |hdl=1911/101830 |hdl-access=free }}</ref>  Some languages such as [[Java programming language|Java]] store matrices using [[Iliffe vector]]s. These are particularly useful for storing [[irregular matrix|irregular matrices]]. Matrices are of primary importance in [[linear algebra]].