Can One Hear the Shape of a Molecule (from its Coulomb Matrix Eigenvalues)?

2020 ◽  
Vol 60 (8) ◽  
pp. 3804-3811 ◽  
Author(s):  
Joshua Schrier
Keyword(s):  
Matrix Eigenvalues ◽  
Coulomb Matrix

scholarly journals Inversion of Tridiagonal Matrices Using the Dunford-Taylor’s Integral

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 870
Author(s):  
Diego Caratelli ◽  
Paolo Emilio Ricci
Keyword(s):  
Functional Analysis ◽  
Computer Algebra ◽  
Toeplitz Matrices ◽  
Test Cases ◽  
Recursive Procedure ◽  
Tridiagonal Matrices ◽  
Special Cases ◽  
The Matrix ◽  
Matrix Eigenvalues ◽  
Complex Valued

We show that using Dunford-Taylor’s integral, a classical tool of functional analysis, it is possible to derive an expression for the inverse of a general non-singular complex-valued tridiagonal matrix. The special cases of Jacobi’s symmetric and Toeplitz (in particular symmetric Toeplitz) matrices are included. The proposed method does not require the knowledge of the matrix eigenvalues and relies only on the relevant invariants which are determined, in a computationally effective way, by means of a dedicated recursive procedure. The considered technique has been validated through several test cases with the aid of the computer algebra program Mathematica©.

Two-body short-range correlations and Coulomb matrix elements

1974 ◽  
Vol 10 (2) ◽  
pp. 931-932 ◽  
Author(s):  
G. F. Bertsch ◽  
S. Shlomo
Keyword(s):  
Short Range ◽  
Matrix Elements ◽  
Coulomb Matrix ◽  
Short Range Correlations

Sensitivity Of matrix eigenvalues

1978 ◽  
Vol 12 (9) ◽  
pp. 1367-1373 ◽  
Author(s):  
George J. Davis ◽  
Cleve B. Moler
Keyword(s):  
Matrix Eigenvalues

scholarly journals An improvement of Ky Fan theorem for matrix eigenvalues

2005 ◽  
Vol 49 (5-6) ◽  
pp. 789-803 ◽  
Author(s):  
Hou-Biao Li ◽  
Ting-Zhu Huang
Keyword(s):  
Fan Theorem ◽  
Matrix Eigenvalues ◽  
Ky Fan ◽  
Ky Fan Theorem
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