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November 21st, 2012, 01:46 PM  #1 
Member Joined: Oct 2012 Posts: 36 Thanks: 0  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 vis 

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