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- #the below is what I directly posted to oBsidian and when it didn't work (please see end) I created a document and pasted it
- $$
- \begin{tabular}{c|c|c|}
- \hline Matrix & Eigenvalues & Eigenvectors \\
- \hline A & $\lambda_{1}, \lambda_{2}, \lambda_{3} \ldots \ldots \lambda_{n}$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
- $k A$ & $k \lambda_{1}, k \lambda_{2}, k \lambda_{3} \ldots \ldots k \lambda_{n}$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
- \hline$A^{m}$ & $\lambda_{1}^{m}, \lambda_{2}^{m}, \lambda_{3}^{m}, \ldots \ldots \lambda_{n}^{m}$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
- $A^{-1}$ & $1 / \lambda_{1}, 1 / \lambda_{2}, 1 / \lambda_{3} \ldots \ldots 1 / \lambda_{n}$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
- \hline$(A)$ & $f(\lambda)$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
- \hline
- \end{tabular}
- $$
- -----------------------------------------------------------------------
- $$
- \documentclass[10pt]{article}
- \usepackage[utf8]{inputenc}
- \usepackage[T1]{fontenc}
- \usepackage{amsmath}
- \usepackage{amsfonts}
- \usepackage{amssymb}
- \usepackage[version=4]{mhchem}
- \usepackage{stmaryrd}
- \title{Properties of Eigenvalues \& Eigenvectors }
- \author{}
- \date{}
- \begin{document}
- \maketitle
- $G \cdot M \cdot(n-\Upsilon)$
- \section*{(1) Sum of the eigenvalues $=$ Trace of the matrix}
- \section*{(2) Product of the eigenvalues $=$ Determinant of the matrix}
- (3) For real matrices, complex eigenvalues occur in complex conjugate pairs.
- \begin{center}
- \begin{tabular}{c|c|c|}
- \hline
- Matrix & Eigenvalues & Eigenvectors \\
- \hline
- A & $\lambda_{1}, \lambda_{2}, \lambda_{3} \ldots \ldots \lambda_{n}$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
- $k A$ & $k \lambda_{1}, k \lambda_{2}, k \lambda_{3} \ldots \ldots k \lambda_{n}$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
- \hline
- $A^{m}$ & $\lambda_{1}^{m}, \lambda_{2}^{m}, \lambda_{3}^{m}, \ldots \ldots \lambda_{n}^{m}$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
- $A^{-1}$ & $1 / \lambda_{1}, 1 / \lambda_{2}, 1 / \lambda_{3} \ldots \ldots 1 / \lambda_{n}$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
- \hline
- $(A)$ & $f(\lambda)$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
- \hline
- \end{tabular}
- \end{center}
- \end{document}
- $$
- and it still didn't work.
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