MathJax

A complex mathematical formuala using MathJax

\[\begin{align*} & \phi(x,y) = \phi \left(\sum_{i=1}^n x_ie_i, \sum_{j=1}^n y_je_j \right) = \sum_{i=1}^n \sum_{j=1}^n x_i y_j \phi(e_i, e_j) = \\ & (x_1, \ldots, x_n) \left( \begin{array}{ccc} \phi(e_1, e_1) & \cdots & \phi(e_1, e_n) \\ \vdots & \ddots & \vdots \\ \phi(e_n, e_1) & \cdots & \phi(e_n, e_n) \end{array} \right) \left( \begin{array}{c} y_1 \\ \vdots \\ y_n \end{array} \right) \end{align*}\]

Unit Circle

Distance between the point on circle and tangent line to x-intercept

\[\begin{align*} Tangent & = \sqrt { \left( {1 \over a} - a \right)^2 + \left( 0 - b \right)^2 } \\ & = \sqrt { \left( {1 \over a^2 } - {2a \over a} +a^2 \right) + b^2} \\ & = \sqrt { {1 \over a^2} - 2 + (a^2 + b^2 ) } \\ & = \sqrt { {1 \over a^2} - 2 + 1} \\ & = \sqrt { {1 \over a^2} - 1} \\ & = \sqrt { (1 - a^2) \over a^2 } \\ & =\sqrt { b^2 \over a^2 } \\ & = { b \over a } \end{align*}\]