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authorsiveshs <siveshs@gmail.com>2010-07-03 04:37:16 +0000
committerbnewbold <bnewbold@adelie.robocracy.org>2010-07-03 04:37:16 +0000
commit825c4cd765a5bfbaa7eb196473a5b4c7410cfd4f (patch)
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downloadafterklein-wiki-825c4cd765a5bfbaa7eb196473a5b4c7410cfd4f.tar.gz
afterklein-wiki-825c4cd765a5bfbaa7eb196473a5b4c7410cfd4f.zip
section 3 editing
-rw-r--r--Fourier Series.page11
1 files changed, 9 insertions, 2 deletions
diff --git a/Fourier Series.page b/Fourier Series.page
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--- 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