Difference between revisions of "Matrices"

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]

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],\quad \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]

@@ Line 8: / Line 8: @@
 a_{21} & a_{22} & a_{23}\\
 a_{31} & a_{32} & a_{33}
+\end{array}\right]
+</math>
+Individual colums and rows are often denoted as column vectors and row vectors. For the example matrix the column vectors are
+:<math>
+\left[
+\begin{array}{c}
+a_{11}\\
+a_{21}\\
+a_{31}
+\end{array}\right],\quad
+\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]
 </math>