Difference between revisions of "Addition of matrices"
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{{Exercise|Selftest: Addition of matrices}} | {{Exercise|Selftest: Addition of matrices}} | ||
| − | 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: | + | 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: |
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:<math> | :<math> | ||
\mathbf{A}+\mathbf{B}= | \mathbf{A}+\mathbf{B}= | ||
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a_{m1}+b_{m1} & \dots & &a_{mn}+b_{mn} | a_{m1}+b_{m1} & \dots & &a_{mn}+b_{mn} | ||
\end{array}\right] | \end{array}\right] | ||
| − | </math | + | </math> |
{{Example | {{Example | ||
Latest revision as of 18:05, 13 November 2015
| ← Back: The transpose of a matrix | Overview: Matrices | Next: Multiplication of matrices → |
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There are exercises as selftest for this article. |
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:
![\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{array}\right]+
\left[\begin{array}{cccc}
b_{11} & b_{12} & \dots &b_{1n} \\
b_{21} &\ddots & &\vdots\\
\vdots & & & \\
b_{m1} & \dots & &b_{mn}
\end{array}\right]=
\left[\begin{array}{cccc}
a_{11}+b_{11} & a_{12}+b_{12} & \dots &a_{1n}+b_{1n} \\
a_{21}+b_{21} &\ddots & &\vdots\\
\vdots & & & \\
a_{m1}+b_{m1} & \dots & &a_{mn}+b_{mn}
\end{array}\right]](/wiki/robotics/images/math/0/0/9/00978381edce5b01bf31dc132eed6331.png)
 Example: Addition of two 3-by-3 matrices
|
![\mathbf{A}_e+\mathbf{B}_e=
\left[\begin{array}{ccc}
1 & 3 & -2\\
0 & -1 & 3\\
2 & 4 & 2
\end{array}\right]+
\left[\begin{array}{ccc}
-3 & 2 & -1\\
2 & 4 & -3\\
0 & -2 & 1
\end{array}\right]=
\left[\begin{array}{ccc}
1-3 & 3+2 & -2-1\\
0+2 & -1+4 & 3-3\\
2+0 & 4-2 & 2-1
\end{array}\right]=
\left[\begin{array}{ccc}
-2 & 5 & -3\\
2 & 3 & 0\\
2 & 2 & 1
\end{array}\right]](/wiki/robotics/images/math/a/8/4/a840860958ad5600280ac623ccd3be01.png)
