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We thank Prof. Robert Schmid for comments on our paper "a new trace bound for a general square matrix product." After thorough thought, we also think theorem 2 of the paper "a new trace bound for a general square matrix product" has no good practical value. We want to clarify that in our paper, we mainly improve the recent results about the trace bounds for the product of two arbitrary real square matrices. Therefore, the title and abstract of our paper do not explicitly refer to Riccati equations. Hence, theorem 2 is only a simple application of the estimated trace bounds.