The author continues his investigations started in [Primitive ideals and symplectic leaves of quantum matrices, Vestn. Samar. Gos. Univ., Mat. Mekh. Fiz. Khim. Biol. 1997, No. 3(6), 81-90 (1997), see also Serdica Math. J. 26, 105-118 (2000; Zbl 0954.17012)]. Let \(\mathcal V\) be the set of complex \(m\times n\) matrices with all minors of maximal order nonzero, let \({\mathbb C}[{\mathcal V}]\) be the algebra of regular functions on \(\mathcal V\) and let \({\mathbb C}_q[{\mathcal V}]\) be the quantum analogue of \({\mathbb C}[{\mathcal V}]\). In the previous papers the author obtained a bijection between the primitive ideals of \({\mathbb C}_q[{\mathcal V}]\) and the symplectic leaves of \(\mathcal V\). In the present paper he calculates the dimensions of these symplectic leaves.