Editing Matrix multiplication (section)

{{Short description|Mathematical operation in linear algebra}}
[[File:Matrix multiplication qtl1.svg|thumb|For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The result matrix has the number of rows of the first and the number of columns of the second matrix.]]
In [[mathematics]], specifically in [[linear algebra]], '''matrix multiplication''' is a [[binary operation]] that produces a [[matrix (mathematics)|matrix]] from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the '''matrix product''', has the number of rows of the first and the number of columns of the second matrix. The product of matrices {{math|'''A'''}} and {{math|'''B'''}} is denoted as {{math|'''AB'''}}.<ref name=":1">{{Cite web|last=Nykamp|first=Duane|title=Multiplying matrices and vectors|url=https://mathinsight.org/matrix_vector_multiplication|access-date=September 6, 2020|website=Math Insight}}</ref>

Matrix multiplication was first described by the French mathematician [[Jacques Philippe Marie Binet]] in 1812,<ref>{{MacTutor|id=Binet|title=Jacques Philippe Marie Binet}}</ref> to represent the [[composition of functions|composition]] of [[linear map]]s that are represented by matrices. Matrix multiplication is thus a basic tool of [[linear algebra]], and as such has numerous applications in many areas of mathematics, as well as in [[applied mathematics]], [[statistics]], [[physics]], [[economics]], and [[engineering]].<ref name="Physics 1991">{{cite book|title=Encyclopaedia of Physics|edition=2nd|first1=R. G. |last1=Lerner|author1-link=Rita G. Lerner | first2= G. L. |last2 = Trigg|publisher=VHC publishers|date=1991|isbn=978-3-527-26954-9}}</ref><ref>{{cite book|title=McGraw Hill Encyclopaedia of Physics|edition=2nd|first=C. B.|last=Parker|date=1994|publisher=McGraw-Hill |isbn=978-0-07-051400-3|url-access=registration|url=https://archive.org/details/mcgrawhillencycl1993park}}</ref>
Computing matrix products is a central operation in all computational applications of linear algebra.