MandysNotes

Monday, 17 March 2014 15:07

Matrices with Latex

By  Gideon
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There are several matrix environments in Latex.

I will start with the "pmatrix" environment.

A very simple 2X2 matrix such as: 

\[\begin{pmatrix}
a_{11} & a_{12} \\
\\
a_{21} & a_{22}
\end{pmatrix}\]

 would be written as follows:

\[\begin{pmatrix}
a_{11} & a_{12} \\
\\
a_{21} & a_{22}
\end{pmatrix}\]

 

 Note that the members of each row are separated by an "&" sign, and that the end of a row is signaled by a "\\."

The last row does not rquire a "\\."

The "\\" between rows is used to create space.

If we entered:

\[\begin{pmatrix}
a_{11} & a_{12} \\
a_{21} & a_{22}
\end{pmatrix}\]

The resulting matrix would look like this:

\[\begin{pmatrix}
a_{11} & a_{12} \\
a_{21} & a_{22}
\end{pmatrix}\]

 

 A 3X3 matrix:


\[ \begin{pmatrix}
a_{11} & a_{12} & a_{13} \\
\\
a_{21} & a_{22} & a_{23} \\
\\
a_{31} & a_{32} & a_{33}
\end{pmatrix} \]

 

is entered as:

\[ \begin{pmatrix}
a_{11} & a_{12} & a_{13} \\
\\
a_{21} & a_{22} & a_{23} \\
\\
a_{31} & a_{32} & a_{33}
\end{pmatrix} \]

 

 Here is an example of a matrix equation from special relativity (a Lorentz boost) using the "pmatrix" environment:

 

\[  \begin{pmatrix}
v'_{0}\\
\\
v'_{1}\\
\\
v'_{2}\\
\\
v'_{3}
\end{pmatrix} = \begin{pmatrix}
\cosh{a} & \sinh{a} & 0 & 0 \\
\\
\sinh{a} & \cosh{a} & 0 & 0\\
\\
0 & 0 & 1 & 0\\
\\
0 & 0 & 0 & 1
\end{pmatrix} \begin{pmatrix}
v_{0}\\
\\
v_{1}\\
\\
v_{2}\\
\\
v_{3}
\end{pmatrix}. \]



 

\[  \begin{pmatrix}
v'_{0}\\
\\
v'_{1}\\
\\
v'_{2}\\
\\
v'_{3} 
\end{pmatrix} = \begin{pmatrix}
\cosh{a} & \sinh{a} & 0 & 0 \\
\\
\sinh{a} & \cosh{a} & 0 & 0\\
\\
0 & 0 & 1 & 0\\
\\
0 & 0 & 0 & 1 
\end{pmatrix} \begin{pmatrix}
v_{0}\\
\\
v_{1}\\
\\
v_{2}\\
\\
v_{3} 
\end{pmatrix}. \]

 Here is the same matrix from the equation above written using the "bmatrix":

\[  \begin{bmatrix}
\cosh{a} & \sinh{a} & 0 & 0 \\
\\
\sinh{a} & \cosh{a} & 0 & 0\\
\\
0 & 0 & 1 & 0\\
\\
0 & 0 & 0 & 1 
\end{bmatrix}\]

 

\[  \begin{bmatrix}
\cosh{a} & \sinh{a} & 0 & 0 \\
\\
\sinh{a} & \cosh{a} & 0 & 0\\
\\
0 & 0 & 1 & 0\\
\\
0 & 0 & 0 & 1 
\end{bmatrix}\]

 
 Here it is with the "vmatrix":

\[  \begin{vmatrix}
\cosh{a} & \sinh{a} & 0 & 0 \\
\\
\sinh{a} & \cosh{a} & 0 & 0\\
\\
0 & 0 & 1 & 0\\
\\
0 & 0 & 0 & 1 
\end{vmatrix}\]

 

\[  \begin{vmatrix}

\cosh{a} & \sinh{a} & 0 & 0 \\
\\
\sinh{a} & \cosh{a} & 0 & 0\\
\\
0 & 0 & 1 & 0\\
\\
0 & 0 & 0 & 1 
\end{vmatrix}\]

 

 This is the "Bmatrix":

 \[  \begin{Bmatrix}
\cosh{a} & \sinh{a} & 0 & 0 \\
\\
\sinh{a} & \cosh{a} & 0 & 0\\
\\
0 & 0 & 1 & 0\\
\\
0 & 0 & 0 & 1 
\end{Bmatrix}\]

 

 \[  \begin{Bmatrix}
\cosh{a} & \sinh{a} & 0 & 0 \\
\\
\sinh{a} & \cosh{a} & 0 & 0\\
\\
0 & 0 & 1 & 0\\
\\
0 & 0 & 0 & 1 
\end{Bmatrix}\]

 

 

This is the "Vmatrix":

 

\[  \begin{Vmatrix}
\cosh{a} & \sinh{a} & 0 & 0 \\
\\
\sinh{a} & \cosh{a} & 0 & 0\\
\\
0 & 0 & 1 & 0\\
\\
0 & 0 & 0 & 1 
\end{Vmatrix}\]

  

 

 \[  \begin{Vmatrix}
\cosh{a} & \sinh{a} & 0 & 0 \\
\\
\sinh{a} & \cosh{a} & 0 & 0\\
\\
0 & 0 & 1 & 0\\
\\
0 & 0 & 0 & 1 
\end{Vmatrix}\]

 

Read 2451 times Last modified on Monday, 17 March 2014 17:54
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