vertical and horizontal equations

Question

I want to write an equation like this (pic related).

What a good way to achieve it in LaTeX?

edit: I'm referring to the vertical math relation and alignment, not to how to get the norms, the boldsymbols or the coloneqq/eqqcolon.

Answer 1

Here's a solution that employs the mathtools, bm, and graphicx packages, with an embedded array environment to house the vertical subcomponent.

\documentclass{article}
\usepackage{mathtools} % for '\coloneqq' and '\DeclarePairedDelimiter' macros
\usepackage{bm}        % for '\bm' macro
\usepackage{graphicx}  % for ' \rotatebox' macro

\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
\newcommand{\rotcoloneqq}{\rotatebox[origin=c]{90}{$\coloneqq$}}

\begin{document}
\[
k_0 \coloneqq \norm{\bm{k}_0} 
= \begin{array}[t]{@{}c@{}}
      \norm{\bm{k}} \\
      \rotcoloneqq \\
      k
  \end{array}
=\frac{2\pi}{\lambda}
\]

\end{document}