An inverse of a real symmetric matrix should in theory return a real symmetric matrix (the same is valid for Hermitian matrices). However, when I compute the inverse with numpy or scipy the returned matrix is asymmetric. I understand that this is due to numerical error. What is the best w...
This paper examines the relationship between 'world citizenship' and the new psychiatric research paradigm established by the World Health Organization in the early post-World War II period. Endorsing the humanitarian ideological concept of 'world citizenship', health professionals called for global ...
I have an expression involving the inverse of a symmetric matrix, which I want to differentiate with respect to one of the elements of that matrix. I've been working through the problem with help from the matrix cookbook (https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf) but am...
If a matrix is symmetric and positive definite, determine if it is invertible and if its inverse matrix is symmetric and positive definite. I know that "if a matrix is symmetric and positive definite, then its inverse matrix is also positive definite", based on a theorem. But I am not su...
AInverseProblemfor ymmetricNonnegativeDefiniteMatricesunder ubmatrixConstraintGONG i-shaT,HU i-yan,ZHANG ei(CollegeofMathematicsand conometrics,HunanUniv,Changsha,Hunan410082,China)Abstract: hispaperdiscussedthenecessaryandsufficientconditionsfortheexistenceofsymmetricnon-negativedefinitesolutionsofamatrixinverse...
AInverseProblemfor ymmetricNonnegativeDefiniteMatricesunder ubmatrixConstraintGONG i-shaT,HU i-yan,ZHANG ei(CollegeofMathematicsand conometrics,HunanUniv,Changsha,Hunan410082,China)Abstract: hispaperdiscussedthenecessaryandsufficientconditionsfortheexistenceofsymmetricnon-negativedefinitesolutionsofamatrixinverse...
, in matrix form. Hermitian matrices can be understood as the complex extension of realsymmetric matrices. If theconjugate transposeof a matrix is denoted by , then the Hermitian property can be written concisely as Hermitian matrices are named afterCharles Hermite, who demonstrated in 1855 that ...
IfAissymmetricacross its main diagonal. ThenA−1is also symmetric. IfAistridiagonal(only three nonzero diagonals),A−1is a dense matrix with no zeros. This is another reason why we don't often compute inverse matrices. The inverse of a band matrix is generally a dense matrix. ...
Each of the four matrices in this formula is either an upper-triangular or a lower-triangular Toeplitz matrix that is generated by either a vector u or a vector v. In the case of the ICZT, a symmetric Toeplitz matrix needs to be inverted. This leads to a simplified formula that ...
1) inverse matrix of modal m matrix 模m矩阵的逆矩阵2) inverse M-matrices 逆M-矩阵 1. Criteria of a special inverse M-matrices; 一类特殊逆M-矩阵的判定 2. We shall prove several inequalies involving symmetric positive semidef-inite,general M-matrices and inverse M-matrices which are ...