Difference between revisions of "Multiplication with a scalar"
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{{Navigation|before=[[Matrices]]|overview=[[Matrices]]|next=[[The transpose of a matrix]]}} | {{Navigation|before=[[Matrices]]|overview=[[Matrices]]|next=[[The transpose of a matrix]]}} | ||
| − | A matrix is multiplied with a scalar by multiplying all the components with the scalar:<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/> |
:<math> | :<math> | ||
| − | + | 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] | ||
</math> | </math> | ||
Revision as of 16:38, 15 May 2014
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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)
