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while working on a combinatorics problem I have found the following result:

let [itex]A=(a_{ij})_{1\leq i,j\leq2n+1}[/itex] where n is a positive integer , be a real Matrix such that :

i) [itex] a_{ij}^2=1-\delta_{ij}[/itex] where [itex] \delta [/itex] is the kronecker symbol

ii) [itex] \forall i \displaystyle{ \sum_{j=1}^{2n+1}a_{ij}=0} [/itex]

then [itex]rankA=2n [/itex]

any idea ?

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# Rank of a matrix

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