In NASA pdf of tensor the author defines a dyad as product of two vectors such that you multiply each components $i,j,k$ with each other components $i,j,k$, i.e. let $v=x_1i +y_1j +z_1k$ and $u=x_2i+y_2j+z_2k$ then a dyad of vectors $vu$ is $x_1x_2+x_1y_2+x_1z_2+y_1x_2+y_1y_2 +\dots$ which can be represented as a square matrix....
later he says that the metric or fundamental tensor(a dyad) is a diagonal matrix...my question is how can a dyad be a diagonal matrix... If we consider a dyad to be dyadic product of two vectors, say $v=(a,b,c)$ and $u=(x,y,z)$, then for the matrix to be diagonal we require product of ay and az to be zero and since the first element of the diagonal ie :ax has a non zero value we conclude $y$ and $z=0$ but if so then the second and third element of the diagonals namely by and $cz$ will also be zero? So how can a diagonal.matrix be a dyad or rank $2$ tensor?