ИСТИНА

We discuss following systems of partial differential equations on the set of pxq-matrices $Z=(z_{kl})$. We take a matrix composed of all partial derivatives $\partial/\partial z_{kl}$, and consider all minors of this matrix of a fixed size $r$. We consider functions annihilated by all such minors (for $p=q=r=2$ we get the John equation). We discuss problems, where such systems arise in a natural way and their properties: $GL(p+q)$-invariance and formulas for all holomorphic solutions in a 'matrix ball' (a set of complex matrices with norm $\le R$).