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Canonical coherent states can be written as infinite series in powers of asingle complex number $z$ and a positive integer $\rho(m)$. The requirementthat these states realize a resolution of the identity typically results in amoment problem, where the moments form the positive sequence of real numbers$\{\rho(m)\}_{m=0}^\infty$. In this paper we obtain new classes of vectorcoherent states by simultaneously replacing the complex number $z$ and themoments $\rho(m)$ of the canonical coherent states by $n \times n$ matrices.Associated oscillator algebras are discussed with the aid of a generalizedmatrix factorial. Two physical examples are discussed. In the first examplecoherent states are obtained for the Jaynes-Cummings model in the weak couplinglimit and some physical properties are discussed in terms of the constructedcoherent states. In the second example coherent states are obtained for aconditionally exactly solvable supersymmetric radial harmonic oscillator.Comment: 18 page

Vector coherent states with matrix moment problems