Velocity0284

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Apr 28th, 2023
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  1. #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
  2.  
  3. $$
  4. \begin{tabular}{c|c|c|}
  5. \hline Matrix & Eigenvalues & Eigenvectors \\
  6. \hline A & $\lambda_{1}, \lambda_{2}, \lambda_{3} \ldots \ldots \lambda_{n}$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
  7. $k A$ & $k \lambda_{1}, k \lambda_{2}, k \lambda_{3} \ldots \ldots k \lambda_{n}$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
  8. \hline$A^{m}$ & $\lambda_{1}^{m}, \lambda_{2}^{m}, \lambda_{3}^{m}, \ldots \ldots \lambda_{n}^{m}$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
  9. $A^{-1}$ & $1 / \lambda_{1}, 1 / \lambda_{2}, 1 / \lambda_{3} \ldots \ldots 1 / \lambda_{n}$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
  10. \hline$(A)$ & $f(\lambda)$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
  11. \hline
  12. \end{tabular}
  13. $$
  14.  
  15. -----------------------------------------------------------------------
  16.  
  17. $$
  18. \documentclass[10pt]{article}
  19. \usepackage[utf8]{inputenc}
  20. \usepackage[T1]{fontenc}
  21. \usepackage{amsmath}
  22. \usepackage{amsfonts}
  23. \usepackage{amssymb}
  24. \usepackage[version=4]{mhchem}
  25. \usepackage{stmaryrd}
  26.  
  27. \title{Properties of Eigenvalues \& Eigenvectors }
  28.  
  29. \author{}
  30. \date{}
  31.  
  32.  
  33. \begin{document}
  34. \maketitle
  35. $G \cdot M \cdot(n-\Upsilon)$
  36.  
  37. \section*{(1) Sum of the eigenvalues $=$ Trace of the matrix}
  38. \section*{(2) Product of the eigenvalues $=$ Determinant of the matrix}
  39. (3) For real matrices, complex eigenvalues occur in complex conjugate pairs.
  40.  
  41. \begin{center}
  42. \begin{tabular}{c|c|c|}
  43. \hline
  44. Matrix & Eigenvalues & Eigenvectors \\
  45. \hline
  46. A & $\lambda_{1}, \lambda_{2}, \lambda_{3} \ldots \ldots \lambda_{n}$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
  47. $k A$ & $k \lambda_{1}, k \lambda_{2}, k \lambda_{3} \ldots \ldots k \lambda_{n}$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
  48. \hline
  49. $A^{m}$ & $\lambda_{1}^{m}, \lambda_{2}^{m}, \lambda_{3}^{m}, \ldots \ldots \lambda_{n}^{m}$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
  50. $A^{-1}$ & $1 / \lambda_{1}, 1 / \lambda_{2}, 1 / \lambda_{3} \ldots \ldots 1 / \lambda_{n}$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
  51. \hline
  52. $(A)$ & $f(\lambda)$ & $X_{1}, X_{2}, X_{3} \ldots \ldots X_{n}$ \\
  53. \hline
  54. \end{tabular}
  55. \end{center}
  56.  
  57.  
  58. \end{document}
  59. $$
  60.  
  61. and it still didn't work.
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