Let
v1,…,vn∈Rmbe a collection of vectors. TheGram matrixof this collection is defined to be the
n-by-
nmatrix whose entry in the
ithrow and
jthcolumn is
aij=vi⋅vj, where
⋅denotes thedot product.
Consider the Gram matrix
Gof the collection:
v1v2v3v4=(1,2,1)=(−3,5,1)=(0,−3,6)=(4,−2,0).
What is the rank of
G?