Display equation in small size and keep the equation number in normal size

Question

My question is: how can I make the equation number of the footnotesize equation desplayed in the normalsize? Currently, the equation number (2) appears too small in footnotesize.

\documentclass[a4paper,11pt]{report}
\usepackage[utf8]{inputenc}
% Math related
\usepackage{amsmath,amssymb}
% matrix spacing
\usepackage{tabstackengine}
\setstackEOL{\cr} 
%%%%%%%%%%%

\begin{document}
This is the normalsize equation. 
    \begin{equation} \label{eq.normal}
    \setstacktabbedgap{1pt}
        \begin{pmatrix} 
            \frac{dF_1(t,\:T_1)}{F_1(t,\:T_1)}\\
            \frac{dF_2(t,\:T_2)}{F_i(t,\:T_2)}\\
            \vdots\\
            \frac{dF_N(t,\:T_N)}{F_N(t,\:T_N)}\\
        \end{pmatrix} =
        \parenMatrixstack{ 
            v_{11} & v_{12} & v_{13}\cr
            v_{21} & v_{22} & v_{23}\cr
            \vdots & \vdots & \vdots\cr
            v_{N1} & v_{N2} & v_{N3}
        }
        \parenMatrixstack{
            \sqrt{\lambda_{1}}&0 & 0\cr
            0 & \sqrt{\lambda_{2}}  & 0\cr
            0 & 0 & \sqrt{\lambda_{3}}
        }
        \begin{pmatrix} 
            dZ_{1}(t)\\
            dZ_{2}(t)\\
            dZ_{3}(t)\\
        \end{pmatrix}
    \end{equation}
\\

This is the footnotesize equation. 
\footnotesize{
        \begin{equation} \label{eq.footnotesize}
        \setstacktabbedgap{1pt}
            \begin{pmatrix} 
                \frac{dF_1(t,\:T_1)}{F_1(t,\:T_1)}\\
                \frac{dF_2(t,\:T_2)}{F_i(t,\:T_2)}\\
                \vdots\\
                \frac{dF_N(t,\:T_N)}{F_N(t,\:T_N)}\\
            \end{pmatrix} =
            \parenMatrixstack{ 
                v_{11} & v_{12} & v_{13}\cr
                v_{21} & v_{22} & v_{23}\cr
                \vdots & \vdots & \vdots\cr
                v_{N1} & v_{N2} & v_{N3}
            }
            \parenMatrixstack{
                \sqrt{\lambda_{1}}&0 & 0\cr
                0 & \sqrt{\lambda_{2}}  & 0\cr
                0 & 0 & \sqrt{\lambda_{3}}
            }
            \begin{pmatrix} 
                dZ_{1}(t)\\
                dZ_{2}(t)\\
                dZ_{3}(t)\\
            \end{pmatrix}
        \end{equation}
    }
\normalsize
\\


\end{document}

Answer 1

Using \footnotesize before an equation is not the best thing to do, because it would impact on the baseline skip of the text before the equation.

I suggest a new environment where you can decide the font size.

\documentclass{article}
\usepackage{amsmath}

\ExplSyntaxOn
\NewDocumentEnvironment{sequation}{O{\small}b}
 {
  \yufip_sequation:nnn {equation}{#1}{#2}
 }{}
\NewDocumentEnvironment{sequation*}{O{\small}b}
 {
  \yufip_sequation:nnn {equation*}{#1}{#2}
 }{}
\cs_new_protected:Nn \yufip_sequation:nnn
 {
  \begin{#1}
  \mbox{#2$\displaystyle#3$}
  \end{#1}
 }
\ExplSyntaxOff

\begin{document}
This is the normalsize equation. 
\begin{equation} \label{eq.normal}
  \begin{pmatrix} 
    \frac{dF_1(t,\:T_1)}{F_1(t,\:T_1)}\\[1ex]
    \frac{dF_2(t,\:T_2)}{F_i(t,\:T_2)}\\
    \vdots\\
    \frac{dF_N(t,\:T_N)}{F_N(t,\:T_N)}\\
  \end{pmatrix} =
  \begin{pmatrix}
    v_{11} & v_{12} & v_{13}\\
    v_{21} & v_{22} & v_{23}\\
    \vdots & \vdots & \vdots\\
    v_{N1} & v_{N2} & v_{N3}
  \end{pmatrix}
  \begin{pmatrix}
    \sqrt{\lambda_{1}}&0 & 0\\
    0 & \sqrt{\lambda_{2}}  & 0\\
    0 & 0 & \sqrt{\lambda_{3}}
  \end{pmatrix}
  \begin{pmatrix} 
    dZ_{1}(t)\\
    dZ_{2}(t)\\
    dZ_{3}(t)\\
  \end{pmatrix}
\end{equation}
This is the footnotesize equation. 
\begin{sequation}[\footnotesize] \label{eq.footnotesize}
  \begin{pmatrix} 
    \frac{dF_1(t,\:T_1)}{F_1(t,\:T_1)}\\[1ex]
    \frac{dF_2(t,\:T_2)}{F_i(t,\:T_2)}\\
    \vdots\\
    \frac{dF_N(t,\:T_N)}{F_N(t,\:T_N)}\\
  \end{pmatrix} =
  \begin{pmatrix}
    v_{11} & v_{12} & v_{13}\\
    v_{21} & v_{22} & v_{23}\\
    \vdots & \vdots & \vdots\\
    v_{N1} & v_{N2} & v_{N3}
  \end{pmatrix}
  \begin{pmatrix}
    \sqrt{\lambda_{1}}&0 & 0\\
    0 & \sqrt{\lambda_{2}}  & 0\\
    0 & 0 & \sqrt{\lambda_{3}}
  \end{pmatrix}
  \begin{pmatrix} 
    dZ_{1}(t)\\
    dZ_{2}(t)\\
    dZ_{3}(t)\\
  \end{pmatrix}
\end{sequation}
This is the small equation, without equation number. 
\begin{sequation*}
  \begin{pmatrix} 
    \frac{dF_1(t,\:T_1)}{F_1(t,\:T_1)}\\[1ex]
    \frac{dF_2(t,\:T_2)}{F_i(t,\:T_2)}\\
    \vdots\\
    \frac{dF_N(t,\:T_N)}{F_N(t,\:T_N)}\\
  \end{pmatrix} =
  \begin{pmatrix}
    v_{11} & v_{12} & v_{13}\\
    v_{21} & v_{22} & v_{23}\\
    \vdots & \vdots & \vdots\\
    v_{N1} & v_{N2} & v_{N3}
  \end{pmatrix}
  \begin{pmatrix}
    \sqrt{\lambda_{1}}&0 & 0\\
    0 & \sqrt{\lambda_{2}}  & 0\\
    0 & 0 & \sqrt{\lambda_{3}}
  \end{pmatrix}
  \begin{pmatrix} 
    dZ_{1}(t)\\
    dZ_{2}(t)\\
    dZ_{3}(t)\\
  \end{pmatrix}
\end{sequation*}

\end{document}