Difference between revisions of "Multiplication of matrices"
From Robotics
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\mathbf{A}\cdot(\mathbf{B})+\mathbf{C})&=\mathbf{A}\cdot\mathbf{B}+\mathbf{A}\cdot\mathbf{C} &\text{for all l-by-m matrices } \mathbf{A} \text{ and m-by-n matrices }\mathbf{B},\mathbf{C} | \mathbf{A}\cdot(\mathbf{B})+\mathbf{C})&=\mathbf{A}\cdot\mathbf{B}+\mathbf{A}\cdot\mathbf{C} &\text{for all l-by-m matrices } \mathbf{A} \text{ and m-by-n matrices }\mathbf{B},\mathbf{C} | ||
\end{align}</math> | \end{align}</math> | ||
+ | |||
+ | {{Example | ||
+ | |Title=Multiplication of several matrices | ||
+ | |Contents=<br/> | ||
+ | A good example for the multiplication of several matrices in the context of robotics and transformations is presented in the robotics script. Please have a look in chapter 3 on page 3-35 | ||
+ | }} |
Revision as of 14:45, 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:
Some further rules for matrix multiplications are:
Example: Multiplication of several matrices
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