I have some simple questions on how to write matrices as tensors.(adsbygoogle = window.adsbygoogle || []).push({});

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]

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# Homework Help: How to write matrices as tensors

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