- #1
JohanL
- 158
- 0
I have some simple questions on how to write matrices as tensors.
1.
[tex]
\left(\begin{array}{cc}a_1\\a_2\end{array}\right)+
\left(\begin{array}{cc}b_1\\b_2\end{array}\right)=
\left(\begin{array}{cc}c_1\\c_2\end{array}\right)
[/tex]
is this equivalent to
[tex]A^j + B^j = C^j[/tex]
with j = 1,2.
2.
[tex]
1/2\left(\begin{array}{cc}\dot{x}_1 & \dot{x}_2\end{array}\right)
\left(\begin{array}{cc}3m & m\\-m & 3m\end{array}\right)
\left(\begin{array}{cc}\dot{x}_1 \\\dot{x}_2\end{array}\right)
[/tex]
is this equivalent to
[tex]
1/2\dot{x}^{\mu}M_{\mu\nu}\dot{x}^{\nu}
[/tex]
[tex]
\mu,\nu=1,2
[/tex]
and
[tex]
M_{11}=3m,...,M_{22}=3m
[/tex]
1.
[tex]
\left(\begin{array}{cc}a_1\\a_2\end{array}\right)+
\left(\begin{array}{cc}b_1\\b_2\end{array}\right)=
\left(\begin{array}{cc}c_1\\c_2\end{array}\right)
[/tex]
is this equivalent to
[tex]A^j + B^j = C^j[/tex]
with j = 1,2.
2.
[tex]
1/2\left(\begin{array}{cc}\dot{x}_1 & \dot{x}_2\end{array}\right)
\left(\begin{array}{cc}3m & m\\-m & 3m\end{array}\right)
\left(\begin{array}{cc}\dot{x}_1 \\\dot{x}_2\end{array}\right)
[/tex]
is this equivalent to
[tex]
1/2\dot{x}^{\mu}M_{\mu\nu}\dot{x}^{\nu}
[/tex]
[tex]
\mu,\nu=1,2
[/tex]
and
[tex]
M_{11}=3m,...,M_{22}=3m
[/tex]