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November 21st, 2012, 12:46 PM   #1
Joined: Oct 2012

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determinant of gram matrix

let gram matrix of vectors v1....vk in V is

<v1,v1> <v1,v2>...<v1,vk>
G(v1,...,vk)= ( .............................. )
<vk,v1> <vk,v2>...<vk,vk>

then prove if v1....vk are linearly dependent then det (G(v1...vk))=0 ,and if v1,...vk are linearly independent then det(G(v1,...,vk))>0

hints:gram matrix is the matrix of <,> restricted to the span of vi-s
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