Then the book I have (commutative algebra by atiyah goes on to say) - That means

[tex] \sum_{j=1}^{n} (\delta_{ij}\phi - a_{ij})x_j=0,\ \delta_{ij}[/tex] being the kronecker delta function This is the part I can't understand - how can you separate [tex]\phi[/tex] form it's argument [tex]x_j[/tex]. How can [tex] \phi(x) = \phi\cdot x[/tex]?