Moore–Penroseinverse;Generalizedinversematrices;Pseudoinversesfornon-invertiblematrices1.IntroductionMoore2(1862–1932)introducedandstudiedthegeneralreciprocalduringthedecade1910–1920.Hestatedtheobjectiveasfollows:‘‘Theeffectivenessofthereciprocalofanonsingularfinitematrixinthestudyofpropertiesofsuchmatricesmakes...
予以确定, 其中是阶方阵. 在历史上, 上面这四个条件是Penrose(就是那位撰写了《皇帝新脑》《通向实在之路》等“科普书”, 并得了诺贝尔物理学奖的Roger Penrose)于1955年最先提出来的(见A generalized inverse for matrices, ...
基于Moore-Penrose广义逆矩阵微分和立体矩阵理论推导了残差向量雅可比矩阵的计算过程;然后,对参数分离后的非线性最小二乘问题利用LM优化方法进行求解,得到非线性参数的迭代方向和最优估值,进而采用最小二乘方法计算线性参数的最优解;最后,通过...
http://mathworld.wolfram.com/Moore-PenroseMatrixInverse.html 显然,埃尔米特矩阵主对角线上的元素都是实数的,其特征值也是实数。对于只包含实数元素的矩阵(实矩阵),如果它是对称阵,即所有元素关于主对角线对称,那么它也是埃尔米特矩阵。也就是说,实对称矩阵是埃尔米特矩阵的特例。
E. Fishkind, The Moore-Penrose Generalized Inverse for Sums of Matrices, SIAM J. Matrix Anal. Appl., Vol. 21, pp. 629-635, 1999.James Allen Fill and Donniell E. Fishkind. The moore-penrose generalized inverse for sums of matrices. SIAM J. Matrix Anal. Appl., 21(2):629-635, ...
1. Definition Moore-penrose inverseA†is the generalization of inverse matrix ofA. If matrixAis non-singular, the moore-penrose inverseA†is exactly the inverse matrixA−1. We will consider a special case. IfmatrixAis positive semidefinite witheigenvaluesλ1,λ2,⋯,λs. That is,A=QDia...
Google Share on Facebook MPGI (redirected fromMoore-Penrose generalized inverse) AcronymDefinition MPGIMicrobial and Plant Genomics Institute(University of Minnesota; St. Paul, MN) MPGIMoore-Penrose Generalized Inverse(linear algebra) MPGIMouvement Pour Guadeloupe Indépendante(French: Movement for an ...
提出了广义实幂等矩阵的概念,研究了它的性质,并给出了其Moore-Penrose广义逆的求法。 2. By using Moore-Penrose generalized inverse and the Kronecker product of matrices, we derive the expression of the least squares symmetric solution of the matrix equation AXB + CYD = E with the least norm. ...
穆尔-彭罗斯广义逆矩阵(Moore-Penrose generalized inverse matrix)是逆矩阵概念的推广,彭罗斯(R.Penrose)证明了对任一m×n阶矩阵A,都存在惟一的n×m阶矩阵X,它满足:1.AXA=A;2.XAX=X;3.(AX)*=AX;4.(XA)*=XA;则称X为A的穆尔-广义逆矩阵,简称M-P逆,记为A⁺。当A为n阶非异阵时,其逆A...