Where is the error in this definition?

I wanted to ask if you could tell me why the formula in the comment area doesn't work in the {defn} area without '%'.

 \begin{defn}
Let $n \times n$ \emph{Hessenberg-Matrix} $\pmb{H}_n$ with coefficients $\beta_j^k$ be

$$\pmb{H_n}=\begin{pmatrix} \beta_0^0 & \beta_1^1 & \cdots &\beta_{n-1}^{n-1}\\ 1 & \ddots & \quad & \vdots\\ \vdots & \ddots \\ 0 & \dots & 1 & \beta_0^{n-1} \end{pmatrix}.$$

%and \pmb{\pi}(t)= $\pi_0(t),\pi_1(t),\dots,\pi_{n-1}(t)$^T
\end{defn}


$...$ is the preferred way to initiate/set a display math equation, rather than $$...$$. See Why is $ ... $ preferable to $$ ... $$?.

Two things you need to change in order for your definition to compile:

1. You need to set math content in math mode, so use $...$ (or $$...$$).

2. Vector notation uses [...], not $...$, which is used for a display math equation (see above).

You're probably after

and $\pmb{\pi}(t) = [ \pi_0(t), \pi_1(t), \dots, \pi_{n-1}(t) ]^T$.


As an aside, keep the document content and structure together by not leaving a blank line between the preceding and following text for a display equation:

Let $n \times n$ \emph{Hessenberg-Matrix} $\pmb{H}_n$ with coefficients $\beta_j^k$ be
$\pmb{H_n} = \begin{pmatrix} \beta_0^0 & \beta_1^1 & \cdots & \beta_{n-1}^{n-1} \\ 1 & \ddots & \quad & \vdots \\ \vdots & \ddots \\ 0 & \dots & 1 & \beta_0^{n-1} \end{pmatrix}$
and $\pmb{\pi}(t) = [ \pi_0(t), \pi_1(t), \dots, \pi_{n-1}(t) ]^T$.

• Rather than \pmb, \bm from the bm package is recommended. – egreg Jul 9 '18 at 21:14