# Vertical space between matrices

I am writing some lecture notes in Econometrics and I want your advice on how to insert some vertical space between two matrices so the result will be easier to follow.

Here is the minimal example:

\documentclass[10pt,a4paper]{article}
\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}

\begin{document}

\begin{align*}
Var(u) &= E(uu') = \\
&= E
\begin{bmatrix}
u_1 u_1' & u_1 u_2' & \cdots & u_1 u_M' \\
u_2 u_1' & u_2 u_2' & \cdots & u_2 u_M' \\
\vdots & & \ddots & \vdots \\
u_M u_1' & u_M u_2' & \cdots & u_M u_M '
\end{bmatrix}
=
\begin{bmatrix}
\sigma_{11} I & \sigma_{12} I  & \cdots & \sigma_{1M} I \\
\sigma_{12} I & \sigma_{22} I  & \cdots & \sigma_{2M} I \\
\vdots &  & \ddots & \vdots\\
\sigma_{1n} I & \sigma_{2M} I & \cdots & \sigma_{MM} I
\end{bmatrix} \\
&=
\begin{pmatrix}
\sigma_{11} & \sigma_{12} & \cdots & \sigma_{1M} \\
\sigma_{12} & \sigma_{22} & \cdots & \sigma_{2M} \\
\vdots &  & \ddots & \vdots \\
\sigma_{1M} & \sigma_{2M} & \cdots & \sigma_{MM}
\end{pmatrix} \otimes I_T
\end{align*}

\end{document}

• You can use \[10pt] or so. (that should be a double backslash) Mar 10, 2014 at 21:18
• @JohnKormylo using that command just before \begin{pmatrix}' does not seem to do the job for me. What exactly do you mean? Thanks in advance. Mar 10, 2014 at 21:33
• Should the term \otimes I_T really be typeset as a subscript to the preceding matrix?
– Mico
Mar 15, 2014 at 9:00
• @MIco No, it is a Kronecker product. Mar 15, 2014 at 23:49

To illustrate @JohnKormylo's comment, you would need to put it in place of the \\ you have already. Changing your MWE (for a gap of 10pt):

\documentclass[10pt,a4paper]{article}
\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}

\begin{document}

\begin{align*}
Var(u) &= E(uu') = \\
&= E
\begin{bmatrix}
u_1 u_1' & u_1 u_2' & \cdots & u_1 u_M' \\
u_2 u_1' & u_2 u_2' & \cdots & u_2 u_M' \\
\vdots & & \ddots & \vdots \\
u_M u_1' & u_M u_2' & \cdots & u_M u_M '
\end{bmatrix}
=
\begin{bmatrix}
\sigma_{11} I & \sigma_{12} I  & \cdots & \sigma_{1M} I \\
\sigma_{12} I & \sigma_{22} I  & \cdots & \sigma_{2M} I \\
\vdots &  & \ddots & \vdots\\
\sigma_{1n} I & \sigma_{2M} I & \cdots & \sigma_{MM} I
\end{bmatrix} \\[10pt]  %%%%%%%%%%%%%%%%% Change this for different spacing
&=
\begin{pmatrix}
\sigma_{11} & \sigma_{12} & \cdots & \sigma_{1M} \\
\sigma_{12} & \sigma_{22} & \cdots & \sigma_{2M} \\
\vdots &  & \ddots & \vdots \\
\sigma_{1M} & \sigma_{2M} & \cdots & \sigma_{MM}
\end{pmatrix}_{\otimes I_T}
\end{align*}

\end{document}\documentclass[]{article}

\begin{document}

\title{Title}
\author{Author}
\date{Today}
\maketitle

Content

\end{document}


You can add space by changing the \\ after \end{bmatrix} into \\[1em], where 1em can be any length. In your example:

\documentclass[10pt,a4paper]{article}
\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}

\begin{document}

\begin{align*}
Var(u) &= E(uu') = \\[1em]
&= E
\begin{bmatrix}
u_1 u_1' & u_1 u_2' & \cdots & u_1 u_M' \\
u_2 u_1' & u_2 u_2' & \cdots & u_2 u_M' \\
\vdots & & \ddots & \vdots \\
u_M u_1' & u_M u_2' & \cdots & u_M u_M '
\end{bmatrix}
=
\begin{bmatrix}
\sigma_{11} I & \sigma_{12} I  & \cdots & \sigma_{1M} I \\
\sigma_{12} I & \sigma_{22} I  & \cdots & \sigma_{2M} I \\
\vdots &  & \ddots & \vdots\\
\sigma_{1n} I & \sigma_{2M} I & \cdots & \sigma_{MM} I
\end{bmatrix} \\[1em]
&=
\begin{pmatrix}
\sigma_{11} & \sigma_{12} & \cdots & \sigma_{1M} \\
\sigma_{12} & \sigma_{22} & \cdots & \sigma_{2M} \\
\vdots &  & \ddots & \vdots \\
\sigma_{1M} & \sigma_{2M} & \cdots & \sigma_{MM}
\end{pmatrix}_{\otimes I_T}
\end{align*}

\end{document}


Here is how I will do it:

\documentclass{article}

\usepackage{mathtools}
\DeclareMathOperator*{\Var}{Var}

\begin{document}

\begin{align*}
\Var(u)
&= E(uu') \\[1ex]
&= E {\mkern -4mu}
\begin{bmatrix}
u_{1}u_{1}' & u_{1}u_{2}' & \cdots & u_{1}u_{M}' \\
u_{2}u_{1}' & u_{2}u_{2}' & \cdots & u_{2}u_{M}' \\
\vdots      &             & \ddots & \vdots      \\
u_{M}u_{1}' & u_{M}u_{2}' & \cdots & u_{M}u_{M}'
\end{bmatrix} \\[1ex]
&= {\mkern -6mu}
\begin{bmatrix}
\sigma_{11}I & \sigma_{12}I & \cdots & \sigma_{1M}I \\
\sigma_{12}I & \sigma_{22}I & \cdots & \sigma_{2M}I \\
\vdots       &              & \ddots & \vdots       \\
\sigma_{1M}I & \sigma_{2M}I & \cdots & \sigma_{MM}I
\end{bmatrix} \\[1ex]
&= {\mkern -6mu}
\begin{pmatrix}
\sigma_{11} & \sigma_{12} & \cdots & \sigma_{1M} \\
\sigma_{12} & \sigma_{22} & \cdots & \sigma_{2M} \\
\vdots      &             & \ddots & \vdots      \\
\sigma_{1M} & \sigma_{2M} & \cdots & \sigma_{MM}
\end{pmatrix}_{\mkern -4mu \otimes I_{T}}
\end{align*}

\end{document}


Note the horizontal spacing improvements using \mkern`.

P.S. I think it doesn't look good with two matrices on the same line in this case.