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I have a huge equation consisting of several matrices. It is stuck together and has to be moved completely between pages causing white spaces in the preceding page. I had to resize it but seems that breaking it is a much better solution. I want to let it break, i.e., e.g. half of at the bottom of one page and the rest in the beginning of the next page. I'm using a double column paper style.

This is what I got,

documentclass[10pt, twocolumn, twoside, journal]{IEEEtran}



%makeatletter

%letIEEEproofproof

%letIEEEendproofendproof

%letproof@undefined

%letendproof@undefined

%makeatother



%letproofrelax

%letendproofrelax



%IEEEoverridecommandlockouts                           

%overrideIEEEmargins



usepackage{amsmath, amsfonts, amssymb, color, enumerate, amsthm, graphicx}

usepackage{tikz, subcaption, cite}

usepackage{color, xcolor, soul, bm}

PassOptionsToPackage{hyphens}{url}usepackage{hyperref}

hypersetup{

  colorlinks   = true, %Colours links instead of ugly boxes

  urlcolor     = blue, %Colour for external hyperlinks

  linkcolor    = blue, %Colour of internal links

  citecolor   = green %Colour of citations

}

usepackage[normalem]{ulem}

newtheorem{problem}{Problem}

newtheorem{theorem}{Theorem}

newtheorem{corollary}{Corollary}

newtheorem{assumption}{Assumption}

newtheorem{proposition}{Proposition}

newtheorem{lemma}{Lemma}

newtheorem{remark}{Remark}

newtheorem{definition}{Definition}

newtheorem{example}{Example}

usepackage{epsfig} 

usepackage{psfrag}

DeclareMathOperator{diag}{diag}

usepackage{tcolorbox}

newcommand{JW}[1]{{color{red}#1}}

include{user_newcommands}



usepackage{algorithm}

usepackage{algpseudocode}

allowdisplaybreaks



%newcommand{ShS}[1]{$clubsuit$footnote{SHREYAS: #1}}

%newcommand{mathcolorbox}[2]{colorbox{#1}{$displaystyle #2$}}



defendtheorem{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}

defendlemma{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}

defendproposition{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}

defendexample{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}

defendremark{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}

defenddefinition{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}

begin{document}

begin{equation}

    resizebox{.45textwidth}{!}{$

    begin{split}

    &L_g^{-1}mathbf{e}_i mathbf{e}_{ij}^{sf T}L_g^{-1} = begin{bmatrix}

    frac{1}{w_1} & 0 & cdots & overbrace{0}^{j^text{th}} & cdots & overbrace{0}^{i^text{th}} & cdots & 0\

    frac{1}{w_1} & frac{1}{w_2} & cdots & 0 & cdots & 0 & cdots & 0\

    vdots & vdots & & vdots & & vdots & & vdots \

    frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & 0 & cdots & 0\

    vdots & vdots & & vdots & & vdots & & vdots\

    frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & 0\

    vdots & vdots & & vdots & & vdots & & vdots\

    frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & frac{1}{w_n}

    end{bmatrix}\

    &times begin{bmatrix}

    0\

    0\

    vdots\

    vdots\

    vdots\

    underbrace{1}_{i^text{th}}\

    vdots\

    0

    end{bmatrix} begin{bmatrix}

    0\

    0\

    vdots\

    underbrace{-1}_{j^text{th}}\

    vdots\

    underbrace{1}_{i^text{th}}\

    vdots\

    0

    end{bmatrix}^{sf T} begin{bmatrix}

    frac{1}{w_1} & 0 & cdots & 0 & cdots & 0 & cdots & 0\

    frac{1}{w_1} & frac{1}{w_2} & cdots & 0 & cdots & 0 & cdots & 0\

    vdots & vdots & & vdots & & vdots & & vdots \

    frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & 0 & cdots & 0\

    vdots & vdots & & vdots & & vdots & & vdots\

    frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & 0\

    vdots & vdots & & vdots & & vdots & & vdots\

    frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & frac{1}{w_n}

    end{bmatrix}\

    &=begin{bmatrix}

    0\

    0\

    vdots\

    0\

    vdots\

    underbrace{frac{1}{w_i}}_{i^text{th}}\

    vdots\

    frac{1}{w_i}

    end{bmatrix} begin{bmatrix}

    0 & cdots & underbrace{0}_{j^text{th}} & frac{1}{w_{j+1}} & frac{1}{w_{j+2}} & cdots & underbrace{frac{1}{w_i}}_{i^text{th}} & 0 & cdots & 0

    end{bmatrix}\

    &=begin{bmatrix}

    0 & 0 & cdots & overbrace{0}^{j^text{th}} & overbrace{0}^{{j+1}^text{th}} & overbrace{0}^{{j+2}^text{th}} & cdots & overbrace{0}^{i^text{th}} & cdots & 0\

    0 & 0 & cdots & 0 & 0 & 0 & cdots & 0 & cdots & 0\

    vdots & vdots & & vdots & vdots & vdots & & vdots & & vdots\

    0 & 0 & cdots & 0 & frac{1}{w_i w_{j+1}} & frac{1}{w_i w_{j+2}} & cdots & frac{1}{w_i^2} & cdots & 0\

    vdots & vdots & & vdots & vdots & vdots & & vdots & & vdots\

    0 & 0 & cdots & 0 & cdots & cdots & cdots & cdots & cdots & 0

    end{bmatrix} geq 0

%}

end{split}

$}

    end{equation}

end{document}