How does the combination of `\huge` and `\bm` work?

Question

I've recently come up with some strange behaviors of simultaneous applications of \huge and \bm. In particular, the results are not consistent depending on the loaded packages.

MWE 1: (with the minimum loaded packages)

\documentclass{article}
\usepackage{mathtools}
\usepackage{bm}

\begin{document}
  $\Delta \qquad \bm{\Delta} \qquad {\Huge\bm{\Delta}}$

  $q \qquad \bm{q} \qquad {\Huge\bm{q}} $ 
\end{document}

Result 1:

In this case, \bm works, but \huge has no influence.

MWE 2: (with the loaded packages corresponding to a specific project of mine)

\documentclass{article}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools}
\usepackage{newtxtext,newtxmath} % for times font
\usepackage[noadjust]{cite}
\usepackage[overload]{empheq} % for subnumbering in cases
\usepackage[framemethod=tikz]{mdframed}
\usepackage{bm}
\usepackage{algorithm}
\usepackage[a4paper, left = 1.5cm, right = 1.5cm, bottom = 1.5cm, top = 1.5cm]{geometry}
\usepackage{braket}
\usepackage[T1]{fontenc}
\usepackage[ansinew,utf8]{inputenc}

\begin{document}
  $\Delta \qquad \bm{\Delta} \qquad {\Huge\bm{\Delta}}$

  $q \qquad \bm{q} \qquad {\Huge\bm{q}} $ 
\end{document}

Result 2:

This one seems even more strange, and the results are somewhat unexpected!

Are these behaviors justifiable?

Edit:

I have a matrix equation, and there is an \underbrace for each matrix. The names of the matrices, e.g., \Delta and q, are about to be put there. But the labels are so small, and I need to make them bigger. What is the best practice to do this?

• scalebox,
• mathlarger,
• ...

\documentclass{article}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools}
\usepackage{newtxtext,newtxmath} % for times font
\usepackage[noadjust]{cite}
\usepackage[overload]{empheq} % for subnumbering in cases
\usepackage[framemethod=tikz]{mdframed}
\usepackage{bm}
\usepackage{algorithm}
\usepackage[a4paper, left = 1.5cm, right = 1.5cm, bottom = 1.5cm, top = 1.5cm]{geometry}
\usepackage{braket}
\usepackage[T1]{fontenc}
\usepackage[ansinew,utf8]{inputenc}

\begin{document}
  \begin{equation}
  \label{eq:vec1}
  \nabla \xi(\bm{q}) = 
  \begin{bmatrix}
  \nabla \xi(q^{0}) \\ \nabla \xi(q^{1}) \\ \nabla \xi(q^{2}) \\ \nabla \xi(q^{3}) \\   \nabla \xi(q^{4}) \\ \nabla \xi(q^{5}) \\ \nabla \xi(q^{6}) 
  \end{bmatrix} = 
  \underbrace{\begin{bmatrix}
    2\lambda_{1}&2\lambda_{3}&2\lambda_{3} &0&0&0&0\\
    2\lambda_{3}&2\lambda_{1}&2\lambda_{3} &0&0&0&0\\
    2\lambda_{3}&2\lambda_{3}&2\lambda_{1} &0&0&0&0\\
    0&0&0&2\lambda_{1}&2\lambda_{3}&0&0\\
    0&0&0&2\lambda_{3}&2\lambda_{1}&0&0\\
    0&0&0&0&0&2\lambda_{1}&2\lambda_{3}\\
    0&0&0&0&0&2\lambda_{3}&2\lambda_{1} 
    \end{bmatrix}}_{\huge\bm{\Lambda}}
  \underbrace{\begin{bmatrix}
    q^{0}\\q^{1}\\q^{2}\\q^{3}\\q^{4}\\q^{5}\\q^{6}
    \end{bmatrix}}_{\huge\bm{q}}
  +2\omega\lambda_{2}
  \underbrace{\begin{bmatrix}
    \mathcal{Q}(q^{0},q^{1}) + \mathcal{Q}(q^{0},q^{2})\\
    \mathcal{Q}(q^{1},q^{0}) + \mathcal{Q}(q^{1},q^{2})\\
    \mathcal{Q}(q^{2},q^{0}) + \mathcal{Q}(q^{2},q^{1})\\
    \mathcal{Q}(q^{3},q^{4})\\
    \mathcal{Q}(q^{4},q^{3})\\
    \mathcal{Q}(q^{5},q^{6})\\
    \mathcal{Q}(q^{6},q^{5})
    \end{bmatrix}}_{\huge\bm{\Omega}}       
  +
  \underbrace{\begin{bmatrix}
    2\bigl(\lambda_{1}q^{0}_{\mathcal{T}} + \lambda_{3}(q^{1}_{\mathcal{T}} + q^{2}_{\mathcal{T}})\bigr)\\
    2\bigl(\lambda_{1}q^{1}_{\mathcal{T}} + \lambda_{3}(q^{0}_{\mathcal{T}} + q^{2}_{\mathcal{T}})\bigr)\\
    2\bigl(\lambda_{1}q^{2}_{\mathcal{T}} + \lambda_{3}(q^{0}_{\mathcal{T}} + q^{1}_{\mathcal{T}})\bigr)\\
    2\bigl(\lambda_{1}q^{3}_{\mathcal{T}} + \lambda_{3}q^{4}_{\mathcal{T}}\bigr)\\
    2\bigl(\lambda_{1}q^{4}_{\mathcal{T}} + \lambda_{3}q^{3}_{\mathcal{T}}\bigr)\\
    2\bigl(\lambda_{1}q^{5}_{\mathcal{T}} + \lambda_{3}q^{6}_{\mathcal{T}}\bigr)\\
    2\bigl(\lambda_{1}q^{6}_{\mathcal{T}} + \lambda_{3}q^{5}_{\mathcal{T}}\bigr)
    \end{bmatrix}}_{\huge\bm{C}} 
  = 0,
  \end{equation}
\end{document}

Answer 1

You get a warning Command \Huge invalid in math mode and the result is thus unpredictable.

Use \textstyle:

\documentclass{article}
\usepackage{newtxtext,newtxmath} % for times font
\usepackage{amsmath}
\usepackage{bm}

\begin{document}

\begin{equation} \label{eq:vec1}
\begin{split}
\nabla \xi(\bm{q}) &=
  \begin{bmatrix}
    \nabla \xi(q^{0}) \\
    \nabla \xi(q^{1}) \\
    \nabla \xi(q^{2}) \\
    \nabla \xi(q^{3}) \\
    \nabla \xi(q^{4}) \\
    \nabla \xi(q^{5}) \\
    \nabla \xi(q^{6}) 
  \end{bmatrix} = 
  {\underbrace{\begin{bmatrix}
    2\lambda_{1}&2\lambda_{3}&2\lambda_{3} &0&0&0&0\\
    2\lambda_{3}&2\lambda_{1}&2\lambda_{3} &0&0&0&0\\
    2\lambda_{3}&2\lambda_{3}&2\lambda_{1} &0&0&0&0\\
    0&0&0&2\lambda_{1}&2\lambda_{3}&0&0\\
    0&0&0&2\lambda_{3}&2\lambda_{1}&0&0\\
    0&0&0&0&0&2\lambda_{1}&2\lambda_{3}\\
    0&0&0&0&0&2\lambda_{3}&2\lambda_{1} 
    \end{bmatrix}}_{\textstyle\bm{\Lambda}}}
  {\underbrace{\begin{bmatrix}
    q^{0}\\q^{1}\\q^{2}\\q^{3}\\q^{4}\\q^{5}\\q^{6}
    \end{bmatrix}}_{\textstyle\bm{q}}}
  \\[2ex]
  &\quad+2\omega\lambda_{2}
  {\underbrace{\begin{bmatrix}
    \mathcal{Q}(q^{0},q^{1}) + \mathcal{Q}(q^{0},q^{2})\\
    \mathcal{Q}(q^{1},q^{0}) + \mathcal{Q}(q^{1},q^{2})\\
    \mathcal{Q}(q^{2},q^{0}) + \mathcal{Q}(q^{2},q^{1})\\
    \mathcal{Q}(q^{3},q^{4})\\
    \mathcal{Q}(q^{4},q^{3})\\
    \mathcal{Q}(q^{5},q^{6})\\
    \mathcal{Q}(q^{6},q^{5})
    \end{bmatrix}}_{\textstyle\bm{\Omega}}}
  +
  {\underbrace{\begin{bmatrix}
    2\bigl(\lambda_{1}q^{0}_{\mathcal{T}} + \lambda_{3}(q^{1}_{\mathcal{T}} + q^{2}_{\mathcal{T}})\bigr)\\
    2\bigl(\lambda_{1}q^{1}_{\mathcal{T}} + \lambda_{3}(q^{0}_{\mathcal{T}} + q^{2}_{\mathcal{T}})\bigr)\\
    2\bigl(\lambda_{1}q^{2}_{\mathcal{T}} + \lambda_{3}(q^{0}_{\mathcal{T}} + q^{1}_{\mathcal{T}})\bigr)\\
    2\bigl(\lambda_{1}q^{3}_{\mathcal{T}} + \lambda_{3}q^{4}_{\mathcal{T}}\bigr)\\
    2\bigl(\lambda_{1}q^{4}_{\mathcal{T}} + \lambda_{3}q^{3}_{\mathcal{T}}\bigr)\\
    2\bigl(\lambda_{1}q^{5}_{\mathcal{T}} + \lambda_{3}q^{6}_{\mathcal{T}}\bigr)\\
    2\bigl(\lambda_{1}q^{6}_{\mathcal{T}} + \lambda_{3}q^{5}_{\mathcal{T}}\bigr)
    \end{bmatrix}}_{\textstyle\bm{C}}} 
  \\
  &= 0,
\end{split}
\end{equation}

\end{document}

You could use \textstyle\mathlarger{\bm{\Lambda}}, but I don't see a real reason for it (requires \usepackage{relsize}).