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The Wikipedia page on symplectic matrices:

http://en.wikipedia.org/wiki/Symplectic_vector_space ,

claims that symplectic matrices are invertible

, i.e., skew-symmetric nxn-

matrix with entries w(b_i,b_j) , satisfying the properties:

i)w(b_i,b_i)=0

ii)w(b_i,b_j)=-w(b_j,b_i)

iii)w(b_i,.)=0 , i.e., w(b_i,b_j)=0 for all b_j

are invertible.

Even for small n , calculating the determinant seems to get out of hand;

Is there an easy way of seeing this?

TIA

Thanks.

iii)w(bi,.)=0 , then bi=0

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# Invertibility of Symplectic Matrices

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