Difference between revisions of "Multiplication with a scalar"
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| + | {{Exercise|Selftest:Multiplication with a scalar}} | ||
A matrix is multiplied with a scalar by multiplying all the components with the scalar. The result is again a matrix:<br/><br/> | A matrix is multiplied with a scalar by multiplying all the components with the scalar. The result is again a matrix:<br/><br/> | ||
Revision as of 14:23, 18 June 2014
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There are exercises as selftest for this article. |
A matrix is multiplied with a scalar by multiplying all the components with the scalar. The result is again a matrix:
![c \cdot \mathbf{A}=c\cdot\left[
\begin{array}{ccc}
a_{11} & a_{12} & a_{13}\\
a_{21} & a_{22} & a_{23}\\
a_{31} & a_{32} & a_{33}
\end{array}\right]=
\left[\begin{array}{ccc}
c\cdot a_{11} & c\cdot a_{12} & c\cdot a_{13}\\
c\cdot a_{21} & c\cdot a_{22} & c\cdot a_{23}\\
c\cdot a_{31} & c\cdot a_{32} & c\cdot a_{33}
\end{array}\right]](/wiki/robotics/images/math/6/0/2/6027948b6a093bc52869c8e78398a7d1.png)
 Example: Multiplying a matrix with a scalar
|
![\begin{align}
\mathbf{A}&=\left[
\begin{array}{ccc}
2 & 3 & 0\\
4 & 1 & 2\\
3 & 1 & 4
\end{array}\right],\quad c=3\\
c \cdot\mathbf{A}&=3\cdot\left[\begin{array}{ccc}
2 & 3 & 0\\
4 & 1 & 2\\
3 & 1 & 4
\end{array}\right]=
\left[\begin{array}{ccc}
3\cdot 2 & 3\cdot 3 & 3\cdot 0\\
3\cdot 4 & 3\cdot 1 & 3\cdot 2\\
3\cdot 3 & 3\cdot 1 & 3\cdot 4
\end{array}\right]=
\left[\begin{array}{ccc}
6 & 9 & 0\\
12 & 3 & 6\\
9 & 3 & 12
\end{array}\right]
\end{align}](/wiki/robotics/images/math/6/3/4/634f14fb3eef7e5bdc4137742c50be34.png)
