Matrix multiplication

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, specifically in <a href="/facts/Linear_algebra/8VaB4VWk">linear algebra</a>, matrix multiplication is a <a href="/facts/Binary_operation/CYtow0bz">binary operation</a> that produces a <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrix</a> 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 A and B is denoted as AB.
</p><p>Matrix multiplication was first described by the French mathematician <a href="/facts/Jacques_Philippe_Marie_Binet/7xEjWJql">Jacques Philippe Marie Binet</a> in 1812, to represent the <a href="/facts/Composition_of_functions/r5Pvnmth">composition</a> of <a href="/facts/Linear_map/Q1PBKNVV">linear maps</a> that are represented by matrices. Matrix multiplication is thus a basic tool of <a href="/facts/Linear_algebra/8VaB4VWk">linear algebra</a>, and as such has numerous applications in many areas of mathematics, as well as in <a href="/facts/Applied_mathematics/qyqklXXm">applied mathematics</a>, <a href="/facts/Statistics/DNPsKGYU">statistics</a>, <a href="/facts/Physics/a7aH2y08">physics</a>, <a href="/facts/Economics/HYctA2Dn">economics</a>, and <a href="/facts/Engineering/RFVg8H3I">engineering</a>.
Computing matrix products is a central operation in all computational applications of linear algebra.
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Matrix multiplication open-in-new

Matrix multiplication