doc/src/Eqs/transform.tex

   1 \documentclass[12pt]{article}
   2
   3 \usepackage{amsmath}
   4
   5 \begin{document}
   6
   7 \begin{eqnarray*}
   8 \begin{pmatrix}
   9 \mathbf{a}  &
  10 \mathbf{b}  &
  11 \mathbf{c}
  12 \end{pmatrix}
  13 & = &
  14 \begin{pmatrix}
  15 a_x & b_x & c_x \\
  16 0 & b_y & c_y \\
  17 0 & 0 & c_z \\
  18 \end{pmatrix} \\
  19 a_x &=& A \\
  20 b_x &=& \mathbf{B} \cdot \mathbf{\hat{A}} \quad = \quad B \cos{\gamma} \\
  21 b_y &=& |\mathbf{\hat{A}} \times \mathbf{B}| \quad = \quad B \sin{\gamma} \quad =  \quad  \sqrt{B^2 - {b_x}^2} \\
  22 c_x &=& \mathbf{C} \cdot \mathbf{\hat{A}} \quad = \quad C \cos{\beta} \\
  23 c_y &=& \mathbf{C} \cdot \widehat{(\mathbf{A} \times \mathbf{B})} \times \mathbf{\hat{A}} \quad = \quad \frac{\mathbf{B} \cdot \mathbf{C} - b_x c_x}{b_y} \\
  24 c_z &=& |\mathbf{C} \cdot \widehat{(\mathbf{A} \times \mathbf{B})}|\quad = \quad \sqrt{C^2 - {c_x}^2 - {c_y}^2} \\
  25 \end{eqnarray*}
  26
  27 \end{document}