Complement of Jacobi matrix

The new properties of Jacobi matrix are discussed. The matrix analogs for the differential operator of the hypergeometric type and of the Pearson one are derived on the base of Jacobi matrix properties exclusivly: the conjugate Sturm system is derived from the properties of symmetric Jacobi matrix $T$, as well as the complementary Jacobi matrix $T^c$, for which this conjugate Sturm system is an ordinary Sturm system.