Showing entries of a vector one after another - latex

Question

Overflow Community! I'm working on a Latex Beamer - Document and I cant think of a nice looking solution for what I am planning to do.
So I have a vector, which entries I want to show one after another. But the right bracket is missing in the first steps when I'm using \pause in my equation, which looks quite ugly. So what I want is both brackets to be visible, while the vectors entries are not. Do you guys have a solution for this?
\documentclass[mathserif, 10pt]{beamer}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,bm,amsthm,graphicx,skmath}
\begin{document}
\begin{frame}
\frametitle{Function $g$}
\[
g(x)=\begin{pmatrix}
g_1(x)\\ \vdots \\ g_n(x) \\ g_{n+1}(x) \\ \vdots \\ g_{2n}(x) \\ g_{2n+1}(x)\\ \vdots \\ g_{3n}(x)
\end{pmatrix}
\pause = \begin{pmatrix}
x_1^2 + x_{n+1}^2 - 1 \\ \vdots \\ x_n^2 + x_{2n}^2 - 1\\ \pause -x_{2n+1}\\ \vdots \\ -x_{3n} \\ \pause x_{2n+1}-L \\ \vdots \\x_{3n}-L
\end{pmatrix}
\]
\end{frame}
\end{document}

Answer 1

\pause is a very crude command, for more fine control you can use commands like \visible<...>{...}.
Please note that you don't need graphicx, amsmath or amsthm with beamer and that the mathserif option is obsolete. This should have caused a warning with a detailed description how this option should be replaced, please don't ignore such warnings.
\documentclass[10pt]{beamer}
\usepackage[utf8]{inputenc}
\usefonttheme[onlymath]{serif}
\usepackage{amsmath,bm,amsthm,
%graphicx,
skmath}
\begin{document}
\begin{frame}
\frametitle{Function $g$}
\[
g(x)=\begin{pmatrix}
g_1(x)\\ \vdots \\ g_n(x) \\ g_{n+1}(x) \\ \vdots \\ g_{2n}(x) \\ g_{2n+1}(x)\\ \vdots \\ g_{3n}(x)
\end{pmatrix}
\visible<2->{ = \begin{pmatrix}
x_1^2 + x_{n+1}^2 - 1 \\ \vdots \\ x_n^2 + x_{2n}^2 - 1\\ \visible<3->{ -x_{2n+1}}\\ \visible<3->{\vdots} \\ \visible<3->{-x_{3n}} \\ \visible<4->{x_{2n+1}-L} \\ \visible<4->{\vdots} \\\visible<4->{x_{3n}-L}
\end{pmatrix}}
\]
\end{frame}
\end{document}

Answer 2

You'll want Beamer's \uncover command, which hides its argument but still makes it take up space:
\[
g(x)=\begin{pmatrix}
g_1(x)\\ \vdots \\ g_n(x) \\ g_{n+1}(x) \\ \vdots \\ g_{2n}(x) \\ g_{2n+1}(x)\\ \vdots \\ g_{3n}(x)
\end{pmatrix}
\pause = \begin{pmatrix}
x_1^2 + x_{n+1}^2 - 1 \\ \vdots \\ x_n^2 + x_{2n}^2 - 1\\ \uncover<3->{-x_{2n+1} \\ \vdots \\ -x_{3n}} \\ \uncover<4->{x_{2n+1}-L \\ \vdots \\x_{3n}-L}
\end{pmatrix}
\]
The bit in the angle brackets (e.g. <3->) indicates that the argument should be uncovered (visible) on frames 3 onwards.
You can also use \visible instead, the difference being:
The \visible command does nearly the same as \uncover. However one difference occurs if the command \setbeamercovered{transparent} has been used to make covered text “transparent” instead, \visible still makes the text completely “invisible” on non-specified slides.