共查询到20条相似文献,搜索用时 570 毫秒
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对于轮换对称问题,最值的取得往往是在对称处,也有很多情形是在非对称处.通过几个实例,进一步探究对称取等的适用条件,避免思维定势,淡化解题技巧,追求通性通法. 相似文献
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给出了三对角行列式的几种算法,利用三对角行列式证明了两类Chebyshev多项式的几种显式. 相似文献
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严格对角占优矩阵的行列式估计 总被引:1,自引:1,他引:0
本文研究了严格对角占优矩阵的行列式估计问题,利用矩阵的逐次降阶法获得了严格对角占优矩阵的几个行列式估计式,并对特殊的严格对角占优矩阵的情形进行了加强. 相似文献
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在文章中,作者给出了块三对角矩阵行列式的一些关系式,本文在,=三基础之上给出了此类矩阵一些类似的关系式. 相似文献
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本文定义了双圆周(bi-circular)随机变量对(或称元素对),并证明其是R-对角的.我们给出了计算两个*-双自由的R-对角随机变量对的乘积对的分布的公式.对于由有限von Neumann代数里的算子组成的左、右作用随机变量对,我们用其随机变量的*-力矩(moments)刻画了R-对角性,定义了η-对角随机变量对,并用其分布的力矩性质刻画了分布的η-对角性. 相似文献
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主要研究了极大加代数的对称代数S上互补基本矩阵,给出本征积的概念,证明了S上的Laplace定理,由此推出所有互补基本矩阵的行列式相等,且任意两个互补基本矩阵的行列式中的非零项均一一对应相等.在一个互补基本矩阵的行列式中,对于确定非零项的任一置换,给出了在另一个互补基本矩阵的行列式中找到置换使其确定相同非零项的方法. 相似文献
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Henryk Minc 《Linear and Multilinear Algebra》1976,4(3):209-215
The general problem considered is: what linear transformations on matrices preserve certain prescribed invariants or other properties of the matrices? Specifically, the forms of the following linear transformations are determined: the linear transformations that hold either the trace or the second elementary symmetric function of the eigenvalues of each matrix fixed, and in addition preserve either the determinant, or the permanent, or an elementary symmetric function of the squares of the singular values, or the property of being a rank 1 matrix or a unitary matrix. 相似文献
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A useful theorem for precisely bounding the infinity norm of the inverse of a five-diagonal symmetric positive definite Toeplitz matrix is obtained. 相似文献
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We present a new symmetric five-diagonal finite difference method for computing eigenvalues of two-point boundary value problems involving a fourth-order differential equation. 相似文献
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We investigate symmetric (0, 1) matrices on which the permanent is convertible to the determinant by assigning ± signs to their entries. In particular, we obtain several quantitative bounds for the number of nonzero elements of such matrices, including the analog of Gibson’s theorem for symmetric matrices. 相似文献
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G. Rousseau 《Linear and Multilinear Algebra》1998,44(2):179-185
It is shown that a matrix with non-negative entries has non-negative determinant if in each row the elements decrease, by steadily smaller amounts, as one proceeds (in either direction) away from the main diagonal. This condition suffices to establish non- negativity of the determinant for certain matrices to which the familiar Minkowski- Hadamard-Ostrowski dominance conditions do not apply. In the symmetric case it provides a sufficient condition for non-negative definiteness. This may be applied to establish the positive definiteness of certain real symmetric Toeplitz matrices. 相似文献
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对称部分为半正定的方阵 总被引:35,自引:0,他引:35
所有n阶具有半正定对称部分的方阵的集合记作PSDn.本文给出了PSDn中方阵在合同下的标准形以及PSDn中两个方阵合同的一个充要条件,并给出了PSDn中一个方阵及其对称部分与斜对称部分的主子式间的一个不等式. 相似文献
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Using determinant representations for partition functions of the corresponding variants of square-ice models and the method recently proposed by one of us, we investigate refined enumerations of vertically symmetric alternating-sign matrices, off-diagonally symmetric alternating-sign matrices, and alternating-sign matrices with a U-turn boundary. For all these cases, we find explicit formulas for refined enumerations. In particular, we prove the Kutin–Yuen conjecture. 相似文献
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We deduce from a determinant identity on quantum transfer matrices of generalized quantum integrable spin chain model their generating functions. We construct the isomorphism of Clifford algebra modules of sequences of transfer matrices and the boson space of symmetric functions. As an application, tau-functions of transfer matrices immediately arise from classical tau-functions of symmetric functions. 相似文献