We shall consider a certain self-adjoint second order matrix equation on an arbitrary time scale so that the special cases of the well-studied corresponding differential equation and the recently developed theory for the related difference equation are unified. This common treatment also shows why the differences between the continuous and the discrete theory occur in the study of this equation. Motivated by the study of variational problems on time scales we examine quadratic functionals and give versions on time scales for the Wronskian identity, Picone's identity, Jacobi's condition, and Sturm's separation and comparison results.

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