Difference between revisions of "Addition of matrices"
From Robotics
| Line 8: | Line 8: | ||
a_{21} &\ddots & &\vdots\\ | a_{21} &\ddots & &\vdots\\ | ||
\vdots & & & \\ | \vdots & & & \\ | ||
| − | a_{m1} & \dots & &a_{mn} | + | a_{m1} & \dots & & a_{mn} |
| − | \end{ | + | \end{array}\right]+ |
| − | \begin{ | + | \left[\begin{array}{cccc} |
b_{11} & b_{12} & \dots &b_{1n} \\ | b_{11} & b_{12} & \dots &b_{1n} \\ | ||
b_{21} &\ddots & &\vdots\\ | b_{21} &\ddots & &\vdots\\ | ||
\vdots & & & \\ | \vdots & & & \\ | ||
b_{m1} & \dots & &b_{mn} | b_{m1} & \dots & &b_{mn} | ||
| − | \end{ | + | \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\\ | |
| − | a_{11} & a_{ | ||
| − | a_{ | ||
\vdots & & & \\ | \vdots & & & \\ | ||
| − | a_{ | + | a_{m1}+b_{m1} & \dots & &a_{mn}+b_{mn} |
| − | \end{ | + | \end{array}\right] |
</math> | </math> | ||
Revision as of 16:56, 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:
![\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)
