2

I have a theorem that contains multiple statements, but the statement is not align in a right way as picture showing
enter image description here

So, how could I improve this problem?

\begin{theorem}

If A is an n × n symmetric matrix, then the following statements hold:

1.A has exactly n real eigenvalues counting for multiplicity.\\

2.The eigenvector corresponding to distinct eigen value are orthogonal.\\

3.A is orthogonal diagonalizable.\\
\end{theorem}
  • Welcome to TeX.SX! Please note that usually it is best to provide a minimal document containing \documentclass and \begin{document}...\end{document} so that those wanting to help you don't have to add that themselves. Also, please note that ending a line with \\ outside of tabular and friends, is usually the wrong thing to do. – Skillmon Nov 29 '20 at 9:41
6

Since it is likely that you have several theorems like that, it is sensible to define a suitable environment for them.

\documentclass{article}
\usepackage{amsmath,amsthm,enumitem}

\newtheorem{theorem}{Theorem}[section]

\newenvironment{statements}
 {\begin{enumerate}[label=\textup{\arabic*.},ref=\arabic*,nosep]}
 {\end{enumerate}}

\begin{document}

\section{Symmetric matrices}

\begin{theorem}
If $A$ is an $n\times n$ symmetric matrix, then the following statements hold:
\begin{statements}
\item $A$ has exactly $n$ real eigenvalues counting for multiplicity;

\item eigenvectors corresponding to distinct eigenvalues are orthogonal;

\item $A$ is orthogonally diagonalizable.
\end{statements}
\end{theorem}

\end{document}

enter image description here

This way, if you change your mind about the typesetting, you can just act in a single place, rather than chasing through your document. For instance, changing nosep into noitemsep would produce

enter image description here

whereas removing nosep altogether would produce

enter image description here

Some stylistic remarks.

  1. The leading item numbers should be upright rather than italic.

  2. Punctuation should be consistent. If you end the preamble with a colon, then the items should be separated by a semicolon or a comma. Capitalizing the first word in an item is optional, but you must be consistent across the whole document.

  3. Even if “A” is a single letter, you must use $A$ or \(A\) because it is a math formula nonetheless.

  4. If you write “eigenvector”, be consistent and also write “eigenvalue”.

  5. “The eigenvector” is (mathematically) wrong: a matrix always has infinitely many eigenvectors relative to a given eigenvalue.

4

You should use an enumerate environment nested inside your theorem:

\documentclass[]{article}

\usepackage{amsthm}
\newtheorem{theorem}{Theorem}

\begin{document}
\begin{theorem}
  If $A$ is an $n\times n$ symmetric matrix, then the following statements hold:
  \begin{enumerate}
    \item $A$ has exactly $n$ real eigenvalues counting for multiplicity.
    \item The eigenvectors corresponding to distinct eigenvalues are orthogonal.
    \item $A$ is orthogonal diagonalizable.
  \end{enumerate}
\end{theorem}
\end{document}

enter image description here

3

You can do:

\begin{theorem}

If $A$ is an $n\times n$ symmetric matrix, then the following statements hold:
\begin{enumerate}
\item $A$ has exactly n real eigenvalues counting for multiplicity.
\item The eigenvector corresponding to distinct eigen value are orthogonal.
\item $A$ is orthogonal diagonalizable.
\end{enumerate}
\end{theorem}

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