Difference between revisions of "Multiplication of matrices"
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{{Navigation|before=[[Addition of matrices]]|overview=[[Matrices]]|next=[[Matrix inversion]]}} | {{Navigation|before=[[Addition of matrices]]|overview=[[Matrices]]|next=[[Matrix inversion]]}} | ||
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+ | 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 <math>\mathbf{A}=(a_{ij})_{i=1...l,j=1...m}</math> with an m-by-n matrix <math>\mathbf{B}=(b_{ij})_{i=1...m,j=1...n}</math> is an l-by-n matrix <math>\mathbf{C}=(c_{ij})_{i=1...l,j=1...n}</math>. The components of the resulting matrix are comuputed as follows:<br/><br/> | ||
+ | :<math> | ||
+ | c_{ij}=\sum^{m}_{k=1}a_{ik}\cdot b_{kj} | ||
+ | </math> | ||
+ | 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> | ||
+ | er | ||
+ | </math> |
Revision as of 14:24, 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: