不可逆矩阵的伴随矩阵的特征值与特征向量的求法 |
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引用本文: | 王莲花,王萍.不可逆矩阵的伴随矩阵的特征值与特征向量的求法[J].河南教育学院学报(自然科学版),2014(1):1-3. |
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作者姓名: | 王莲花 王萍 |
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作者单位: | [1] 北京物资学院信息学院,北京通州101149 [2] 孔集乡第一中学数学组,河南宁陵476712 |
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基金项目: | 北京物资学院专业建设--信息类专业群建设(PXM2012_014214_000022) |
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摘 要: | 给出矩阵A不可逆时,其伴随矩阵A*的特征值和特征向量的简便求法,即当r(A*)=0时,A*的所有的特征值都为零,任一非零向量都是其特征向量;当r(A*)=1时,A*有n-1个特征值为0,另一个特征值为A11+A22+…+Ann,此时,若A11+A22+…+Ann=0,则A*的属于特征值为0的所有特征向量由A的n-1个线性无关的列向量生成;若A11+A22+…+Ann≠0,A*的属于特征值为0的所有特征向量由A的n-1个线性无关的列向量生成,属于A11+A22+…+Ann的特征向量由A*的行元素的比例系数组成.
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关 键 词: | 不可逆矩阵 伴随矩阵 特征值 特征向量 |
The Method of Eigenvalues and Eigenvectors about Adjoin Matrix of Irreversible Matrix |
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Institution: | WANG Lian-hua WANG Pin ( 1. College of Information, Beijing Wuzi University, Beijing 101149, China ; 2. Mathematics Group, First Middle School of Kongji Township, Ningling 476712, China) |
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Abstract: | The simple and convenient method of eigenvalues and eigenvectors about adjoint matrix of irreversible matrix is given when the matrix A is irreversible matrix. That is, if r(A * ) = 0, then all the eigenvalues of A * is zero. If r(A " ) = 1, n - 1 eigenvalues ofA * are zero, and another eigenvalue is A1l +A22 + ... +Ann. At this time, if All + A2z +-.. + Ann = 0, all the eigenvectors of A * belonging to zero eigenvalue are generated from n -1 linearly independent column A. If All +A22 +--. + Ann 50, the eigenvectors of A * belonging to zero eigenvalue are gene- rated of n- 1 linearly independent column A, and the linearly independent eigenvectors of A * belonging to AN +A22 + .... + Ana are composed by matrix A line element proportionality coefficient. |
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Keywords: | irreversible matrix adjoint matrix eigenvalue eigenvector |
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