section 3 editing

1 files changed, 9 insertions, 2 deletions

diff --git a/Fourier Series.page b/Fourier Series.page
index e603e15..7e3522b 100644
--- a/Fourier Series.page
+++ b/Fourier Series.page
@@ -138,9 +138,16 @@ which is the condition of orthonormality (the vectors are perpendicular and each
 ##Determining Coefficients of the Basis vectors
 In any vector space, the inner product of a vector and its basis vector gives the coefficient. For example, consider a 2-dimensional vector as shown below:
 
---> image of a 2d vector
+[Graph of a vector](/vector.gif)
 
---> demo of coefficient being true
+The above vector $\vec v$ can be expressed in terms of the basis vectors $\vec e1$ and $\vec e2$ as follows:
+$$
+\begin{array}{ccl}
+\vec v & = & a_1 \, \vec e1 + a_2 \, \vec e2\\
+& = &    a_1 \,     \begin{array}{c}1\\0\end{array}   + a_2 \,    \begin{array}{c}0\\1\end{array}\\
+& = &    \begin{array}{c}a_1\\a_2\end{array}
+\end{array}
+$$
   
 Extending this principle to the case of an n-dimensional vector:
 --> compute inner product here and then continue to show what the coefficient formula is