For this purpose, we should first find eigenvalue(s) and corresponding eigenvector(s) of the matrix. Depending upon the nature of matrices, we get various canonical forms of matrices such as a triangle matrix and a diagonal matrix . Regarding any form of matrices, we can treat these ...
1. This paper describes the orthogonal matrix canonical forms for matrices and the orthogonal matrix decomposition form. 给出了正交矩阵的相似标准形及正交矩阵的分解形式。2) matrix similarity canonical form 矩阵相似标准形 1. With regard to the value and difficulty of research on matrices over ...
Square complex matrices A, B are said to be consimilar if A=SBS̄−1 for some nonsingular matrix S. Consimilarity is an equivalence relation that is a natural matrix generalization of rotation of scalars in the complex plane. We survey the known forms to which a given complex matrix ...
1. Introduction This paper exhibits a constructive method for deriving canonical froms for Hamilto- nian and symplectic matrices under conjugation by symplectic matrices. Special care has been taken to treat the case of real canonical forms in detail. The basic result for a real Hamiltonian or ...
Canonical forms for congruence of matrices and T-palindromic matrix pencils: a tribute to H. W. Turnbull and A. C. Aitken A canonical form for congruence of matrices was introduced by Turnbull and Aitken in 1932. More than 70 years later, in 2006, another canonical form for co... D ...
Classroom Note: A Unified Elementary Approach to Canonical Forms of Matrices 来自 国家科技图书文献中心 喜欢 0 阅读量: 29 作者: John Karro and Chi-Kwong Li 摘要: A unified elementary approach is used to obtain various canonical-form theorems for complex and real matrices. 关键词: canonical ...
Those canonical forms are obtained as an application of a more general method to select canonical elements Mc in the orbits OM of a matrix group G acting on a set of matrices M⊂Cl·p. We define a total order (≺) on Cl·p,...
关键词 多项式矩阵,合同,对称矩阵,反对称矩阵 Congruent Canonical Forms of Symmetric and Skew-Symmetric Polynomial Matrices Qi Si, Yunbo Tian School of Mathematics and Statistics, Linyi University, Linyi Shandong th th rd Received: Apr. 14 , 2022; accepted: May 16 , 2022; published: May 23 , ...
As special cases of our canonical forms, we obtain – in a coherent and systematic way – known canonical forms for conjugate normal, congruence normal, coninvolutory, involutory, projection, λ-projection, and unitary matrices. But we also obtain canonical forms for matrices whose squares are...
forcomplexmatricesAsuchthat¯AA(respectively,A2)isnormal.Asspecialcasesofourcanonicalforms,weobtain—inacoherentandsystematicway—knowncanonicalformsforconjugatenormal,congruencenormal,coninvolutory,involutory,projection,λ-projection,andunitarymatrices.ButwealsoobtaincanonicalformsformatriceswhosesquaresareHermitian...