`hyperplaneOrthogonalVector` <-
function( X=diag(rep(1,3)) ){
k <- ncol(X)
d <- numeric(k)
v <- rep(1,k)
Y <- X
for (i in 1:k){
Y[,i] <- v
d[i] <- det(Y)
Y[,i] <- X[,i]
}
return(d)
}
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