Difference between revisions of "Matrices"
From Robotics
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a_{21}\\ | a_{21}\\ | ||
a_{31} | a_{31} | ||
| − | \end{array}\right], | + | \end{array}\right], |
\left[ | \left[ | ||
\begin{array}{c} | \begin{array}{c} | ||
Revision as of 15:24, 15 May 2014
This article deals with some fundamental matrix features and the basic arithmetic operations.
Matrices can have arbitrary dimensions. In the context of robotics mainly 3-by-3 or 4-by-4 matrices are used. An example of a 3-by-3 matrix is:
![\mathbf{M}=\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]](/wiki/robotics/images/math/1/f/2/1f29be7647766c2d6f89f2f2f0217819.png)
Individual colums and rows are often denoted as column vectors and row vectors. For the example matrix the column vectors are
![\left[
\begin{array}{c}
a_{11}\\
a_{21}\\
a_{31}
\end{array}\right],
\left[
\begin{array}{c}
a_{12}\\
a_{22}\\
a_{32}
\end{array}\right],\text{and }
\left[
\begin{array}{c}
a_{13}\\
a_{23}\\
a_{33}
\end{array}\right]](/wiki/robotics/images/math/2/1/9/2198ba7778b8f7508d3ac527dac237a3.png)
