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用数学归纳法推出了可逆矩阵的高次伴随矩阵的公式,并结合可逆矩阵的基本公式得出了可逆矩阵的高次伴随矩阵的行列式和逆矩阵,给出了可逆矩阵的高次伴随矩阵的特征值和特征向量的表示公式,最后讨论了若干个可逆矩阵的乘积的高次伴随矩阵. 相似文献
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本文主要讨论二阶分块矩阵的伴随矩阵,考虑到任何矩阵无论是否可逆,均存在伴随矩阵,将文献[1]中可逆的情况推广到了较一般情况,得到了二阶分块矩阵伴随矩阵的有关结论,并改进了文献[2]中相关结论的证明过程. 相似文献
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研究了格矩阵的行列式与伴随矩阵,给出了它们的一些代数性质,同时给出了由一个格矩阵构造一个传递矩阵的方法. 相似文献
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本文研究了一类特殊的逆M-矩阵.利用有向图中的性质和方法,获得了逆M-矩阵其逆为三对角矩阵的充分必要条件,推广了常见的D-型矩阵,得到了一类矩阵为逆M-矩阵的条件. 相似文献
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粗糙集的矩阵关系 总被引:1,自引:0,他引:1
罗来鹏 《数学的实践与认识》2009,39(23)
将粗糙集中的集合转化为矩阵刻画,通过引入矩阵算子、类矩阵算子,借助截矩阵和关系矩阵,讨论了Paw lak粗糙集和变精度粗糙集中集合关系的矩阵计算及其所具有的一些基本性质. 相似文献
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高玉芬 《数学的实践与认识》2009,39(13)
跳行范德蒙矩阵是一种重要的矩阵,在函数插值等方面有着重要的应用.根据跳行范德蒙矩阵的特殊结构,将跳行范德蒙矩阵分解为一系列下三角矩阵与一系列上三角矩阵的乘积.进一步给出了其逆矩阵分解为一系列上三角矩阵与一系列下三角矩阵的乘积的表达式. 相似文献
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通过研究矩阵A与伴随矩阵A<'*>,陪同矩阵<'*>A之间的关系,给出陪同矩阵<'*>A的一些性质. 相似文献
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A new chaotic cryptosystem 总被引:6,自引:0,他引:6
Based on the study of some previously proposed chaotic encryption algorithms, we found that it is dangerous to mix chaotic state or iteration number of the chaotic system with ciphertext. In this paper, a new chaotic cryptosystem is proposed. Instead of simply mixing the chaotic signal of the proposed chaotic cryptosystem with the ciphertext, a noise-like variable is utilized to govern the encryption and decryption processes. This adds statistical sense to the new cryptosystem. Numerical simulations show that the new cryptosystem is practical whenever efficiency, ciphertext length or security is concerned. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2010,15(7):1887-1892
This paper introduces two different types of attacks on a recently proposed cryptosystem based on chaotic standard and logistic maps. In the two attacks, only a pair of (plaintext/ciphertext) was needed to totally break the cryptosystem. 相似文献
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Stefan Veldsman 《代数通讯》2017,45(6):2505-2519
The radicals of full matrix rings as well as structural matrix rings have been studied extensively and there is a well-developed theory for both. Here we initiate the radical theory for another class of matrix rings over a given ring; the matrix ring generated by the companion matrix of a polynomial over the ring. 相似文献
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Eraj Khan Ernst Gabidulin Bahram Honary Hassan Ahmed 《Designs, Codes and Cryptography》2014,70(1-2):231-239
GPT public key cryptosystem was proposed by Gabidulin, Paramonov and Tretjakov in 1991. This cryptosystem is based on rank error correcting codes. The main advantage of using rank codes in cryptography is that, it has smaller key size as compared to other code based public key cryptosystems. Several attacks against this system were published and some modifications were also proposed withstanding these attacks. In this paper, we have proposed a modified Niederreiter type GPT cryptosystem based on reducible rank codes by properly choosing the column scrambler matrix to withstand these attacks. Although, the idea of choosing column scrambler matrix from extension field is not new but the approach proposed in this paper, provides more elements of column scrambler matrix from extension field as compared to any previous modifications which makes system more secure against attacks. 相似文献
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定义广义四元数共轭延拓矩阵的概念,利用矩阵分块和四元数矩阵的实表示方法,分别给出四元数矩阵方程AX=C和XB=D存在列共轭延拓解和行共轭延拓解的必要充分条件及解的表达式. 相似文献
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Stable iterations for the matrix square root 总被引:3,自引:0,他引:3
Nicholas J. Higham 《Numerical Algorithms》1997,15(2):227-242
Any matrix with no nonpositive real eigenvalues has a unique square root for which every eigenvalue lies in the open right half-plane. A link between the matrix sign function and this square root is exploited to derive both old and new iterations for the square root from iterations for the sign function. One new iteration is a quadratically convergent Schulz iteration based entirely on matrix multiplication; it converges only locally, but can be used to compute the square root of any nonsingular M-matrix. A new Padé iteration well suited to parallel implementation is also derived and its properties explained. Iterative methods for the matrix square root are notorious for suffering from numerical instability. It is shown that apparently innocuous algorithmic modifications to the Padé iteration can lead to instability, and a perturbation analysis is given to provide some explanation. Numerical experiments are included and advice is offered on the choice of iterative method for computing the matrix square root. 相似文献
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提出了一种改进的梯度迭代算法来求解Sylvester矩阵方程和Lyapunov矩阵方程.该梯度算法是通过构造一种特殊的矩阵分裂,综合利用Jaucobi迭代算法和梯度迭代算法的求解思路.与已知的梯度算法相比,提高了算法的迭代效率.同时研究了该算法在满足初始条件下的收敛性.数值算例验证了该算法的有效性. 相似文献
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《Linear and Multilinear Algebra》2012,60(1):1-28
ABSTRACTIn recent years, special matrix functions and polynomials of a real or complex variable have been in a focus of increasing attention leading to new and interesting problems. In this work, we present matrix space analogues to generalized some functions and polynomials in the framework of matrix setting. Many of the special matrix functions and polynomials are constructed along standard procedures. Recently published papers are also surveyed and we list the most essential ones. 相似文献