Difference between revisions of "Addition of matrices"
From Robotics
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Requirement for the addition of two matrices is, that they have the same number of rows and the same number of colums. So both matrices have to be an m-by-n matrix. The addition is made by adding each the components:<br/><br/> | Requirement for the addition of two matrices is, that they have the same number of rows and the same number of colums. So both matrices have to be an m-by-n matrix. The addition is made by adding each the components:<br/><br/> | ||
:<math> | :<math> | ||
| − | + | \mathbf{A}+\mathbf{B}= | |
| + | \left[\begin{array}{cccc} | ||
| + | a_{11} & a_{12} & \dots &a_{1n} \\ | ||
| + | a_{21} &\ddots & &\vdots\\ | ||
| + | \vdots & & & \\ | ||
| + | a_{m1} & \dots & &a_{mn} | ||
| + | \end{pmatrix}\right]+ | ||
| + | \begin{pmatrix} | ||
| + | b_{11} & b_{12} & \dots &b_{1n} \\ | ||
| + | b_{21} &\ddots & &\vdots\\ | ||
| + | \vdots & & & \\ | ||
| + | b_{m1} & \dots & &b_{mn} | ||
| + | \end{pmatrix} | ||
| + | , \quad | ||
| + | \mathbf{A}^T = | ||
| + | \begin{pmatrix} | ||
| + | a_{11} & a_{21} & \dots &a_{m1} \\ | ||
| + | a_{12} &\ddots & &\vdots\\ | ||
| + | \vdots & & & \\ | ||
| + | a_{1n} & \dots & &a_{mn} | ||
| + | \end{pmatrix} | ||
</math> | </math> | ||
Revision as of 16:53, 15 May 2014
| ← Back: The transpose of a matrix | Overview: Matrices | Next: Multiplication with a vector → |
Requirement for the addition of two matrices is, that they have the same number of rows and the same number of colums. So both matrices have to be an m-by-n matrix. The addition is made by adding each the components:
- Failed to parse (syntax error): \mathbf{A}+\mathbf{B}= \left[\begin{array}{cccc} a_{11} & a_{12} & \dots &a_{1n} \\ a_{21} &\ddots & &\vdots\\ \vdots & & & \\ a_{m1} & \dots & &a_{mn} \end{pmatrix}\right]+ \begin{pmatrix} b_{11} & b_{12} & \dots &b_{1n} \\ b_{21} &\ddots & &\vdots\\ \vdots & & & \\ b_{m1} & \dots & &b_{mn} \end{pmatrix} , \quad \mathbf{A}^T = \begin{pmatrix} a_{11} & a_{21} & \dots &a_{m1} \\ a_{12} &\ddots & &\vdots\\ \vdots & & & \\ a_{1n} & \dots & &a_{mn} \end{pmatrix}
