From 825c4cd765a5bfbaa7eb196473a5b4c7410cfd4f Mon Sep 17 00:00:00 2001 From: siveshs Date: Sat, 3 Jul 2010 04:37:16 +0000 Subject: section 3 editing --- Fourier Series.page | 11 +++++++++-- 1 file 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 -- cgit v1.2.3