| Matrix theory which is a fundamental tool in Mathematics has been an important tool in some technologic fields .And estimate of eigenvalue which is a significant part in Matrix theory plays an important role in some relevant fields such as Statistics, Numerical analysis, System engineering, Stability theory,Computation methods, etc.In this paper,first of all, we discussed the problem of nonsingularity of complex partitioned matrices, gave the conditions of complex partitioned matrices and irreducible partitioned matrices. In addition, we obtained the new criteria for a matrix to be a positive stable matrix. Therefore, we provide a new method solving Differential equations in Vibrating systems by these results.
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