Let be vectors in ; let be a matrix . If is an arbitrary -tuple from the set , show that

,

where

for

Please help or give a hint

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- Dec 5th 2012, 11:05 PMvercammenTopology. Matrix question
Let be vectors in ; let be a matrix . If is an arbitrary -tuple from the set , show that

,

where

for

Please help or give a hint - Feb 3rd 2013, 03:30 AMtommyjbabyRe: Topology. Matrix question
write out the definition of the wedge product. then write out your vectors in the basis ej. Then using what you have above, and the fact that each phi i is linear, you realise that the only non zero component in your sum is when each phi i is applied to just ei. ie. phi1(e1).phi2(e2)...but this is just the definition of the determinant of the matrix X