LaTeX macro examples


#Equation

\begin{align*}
x^2 + y^2 &= 1 \\
y &= \sqrt{1 - x^2}
\end{align*}

#Matrix operation

C=A+BD=A⋅B\begin{align*} C &= A + B \\ D &= A \cdot B \end{align*}CD=A+B=AB

#Left aligned

x2+y2=1y=1−x2\begin{align*} x^2 + y^2 &= 1 \\ y &= \sqrt{1 - x^2} \end{align*}x2+y2y=1=1x2

#Inline

The photon traces a longer diagonal path, so the same tick stretches to

\Delta t = \gamma\,\Delta t_0
where the Lorentz factor is
\gamma = (1 - v^2/c^2)^{-1/2}
. Because velocity is always below light speed,
v/c < 1
and so
\gamma \geq 1
always, growing without bound as
v \to c
. At everyday speeds
\gamma \approx 1
and the effect vanishes. Cosmic-ray muons make this concrete. With a rest-frame lifetime of
\tau_0 \approx 2.2\,\mu s
they should decay long before reaching the ground, yet we detect them at sea level. Travelling at
v \approx 0.998c
gives
\gamma \approx 15.8
, stretching their observed lifetime to
\Delta t \approx 35\,\mu s
- just long enough to survive the trip.

The photon traces a longer diagonal path, so the same tick stretches to

\Delta t = \gamma\,\Delta t_0
where the Lorentz factor is
\gamma = (1 - v^2/c^2)^{-1/2}
. Because velocity is always below light speed,
v/c < 1
and so
\gamma \geq 1
always, growing without bound as
v \to c
.


#Large Inline

this is some latex text before

E = mc^2
and afterwards, this is some latex text before
E = mc^2
and afterwards, this is some latex text before
E=mc^2\begin{pmatrix}12 & 12 & 3\\ 5 & 4 & 3\\ f & 3 & e\end{pmatrix}
and afterwards, this is some latex text before
E = mc^2
and afterwards,