Editing Pascal's triangle (section)

=== Construction as matrix exponential ===
{{Image frame|caption=Binomial matrix as matrix exponential. All the dots represent 0.
|content=<math>\begin{align}
\exp\begin{pmatrix}
. & . & . & . & . \\
1 & . & . & . & . \\
. & 2 & . & . & . \\
. & . & 3 & . & . \\
. & . & . & 4 & .
\end{pmatrix} &=
\begin{pmatrix}
1 & . & . & . & . \\
1 & 1 & . & . & . \\
1 & 2 & 1 & . & . \\
1 & 3 & 3 & 1 & . \\
1 & 4 & 6 & 4 & 1
\end{pmatrix}\\
e^{\text{counting}} &= \text{binomial}
\end{align}
</math>
}}
{{See also|Pascal matrix}}
Due to its simple construction by factorials, a very basic representation of Pascal's triangle in terms of the [[matrix exponential]] can be given: Pascal's triangle is the exponential of the matrix which has the sequence 1, 2, 3, 4, ... on its sub-diagonal and zero everywhere else.