# What is a determined system of linear PDEs?

When it comes to a system of linear equations, - it is determined when it has $$N$$ variables and $$N$$ linearly independent equations.

If the equations are less, it is underdetermined; if more, it is overdetermined.

What about a system of linear PDEs?

Example: $$f = f(x_1,x_2,...,x_N)$$

The PDE system contains all first-order derivatives $$\frac{\partial f}{\partial x_1}, \frac{\partial f}{\partial x_2}, ..., \frac{\partial f}{\partial x_N}$$.

The PDE system is linear.

What conditions are to be met by the PDE system for it to have an unique solution?