We study the operator A\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {A}$$\end{document} of multiplication by an independent variable in a matrix Sobolev space W2(M)\documentclass[12pt]{minimal}
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\begin{document}$$W^2(M)$$\end{document}. In the cases of finite measures on [a, b] with (2×2)\documentclass[12pt]{minimal}
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\begin{document}$$(2\times 2)$$\end{document} and (3×3)\documentclass[12pt]{minimal}
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\begin{document}$$(3\times 3)$$\end{document} real continuous matrix weights of full rank it is shown that the operator A\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {A}$$\end{document} is symmetrizable. Namely, there exist two symmetric operators B\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {B}$$\end{document} and C\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {C}$$\end{document} in a larger space such that Af=CB-1f\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {A} f = \mathcal {C} \mathcal {B}^{-1} f$$\end{document}, f∈D(A)\documentclass[12pt]{minimal}
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\begin{document}$$f\in D(\mathcal {A})$$\end{document}. As a corollary, we obtain some new orthogonality conditions for the associated Sobolev orthogonal polynomials. These conditions involve two symmetric operators in an indefinite metric space.
