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引入次M-矩阵与逆次M-矩阵的概念,讨论了二者上的Hadamard-Fischer不等式,并改进了Hadamard不等式的结果,即对任一非奇异n阶次M-矩阵A都满足| det A |≤min{nⅡi=1 an-i+1 i- max1≠σ∈Sn(nⅡi=1an-σ(i)+1ian-i+1 σ(i))1/2,min(an-k+1knⅡi=1i≠k(an-i+1i-an-k+1 ian-i+1 k/an-k+1 k))}.