Difference between revisions of "Multiplication of matrices"
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For example the multiplication of a 2-by-3 matrix with a 3-by-2 matrix results in a 2-by-2 matrix and is computed as follows:<br/><br/> | For example the multiplication of a 2-by-3 matrix with a 3-by-2 matrix results in a 2-by-2 matrix and is computed as follows:<br/><br/> | ||
:<math> | :<math> | ||
− | + | \mathbf{A}\cdot\mathbf{B}= | |
+ | \left[\begin{array}{ccc} | ||
+ | a_{11} & a_{12} & a_{13} \\ | ||
+ | a_{21} & a_{22} & a_{23} | ||
+ | \end{array}\right]\cdot | ||
+ | \left[\begin{array}{cc} | ||
+ | b_{11} & b_{12} \\ | ||
+ | b_{21} & b_{22}\\ | ||
+ | b_{31} & b_{32} | ||
+ | \end{array}\right]= | ||
+ | \left[\begin{array}{cc} | ||
+ | a_{11}\cdot b_{11}+a_{12}\cdot b_{21}+a_{13}\cdot b_{31} & a_{11}\cdot b_{12}+a_{12}\cdot b_{22}+a_{13}\cdot b_{12} \\ | ||
+ | a_{21}\cdot b_{11}+a_{22}\cdot b_{21}+a_{23}\cdot b_{31} & a_{21}\cdot b_{12}+a_{22}\cdot b_{22}+a_{23}\cdot b_{12} | ||
+ | \end{array}\right] | ||
</math> | </math> |
Revision as of 14:29, 16 May 2014
← Back: Addition of matrices | Overview: Matrices | Next: Matrix inversion → |
Two matrices can be multiplied if the number of colums of the left matrix equals the number of rows of the right matrix. The result of the multiplication of an l-by-m matrix with an m-by-n matrix is an l-by-n matrix . The components of the resulting matrix are comuputed as follows:
For example the multiplication of a 2-by-3 matrix with a 3-by-2 matrix results in a 2-by-2 matrix and is computed as follows: