Open AccessSolution of symmetric positive semidefinite Procrustes problem
Author(s) -
Jingjing Peng,
Qingwen Wang,
Zhenyun Peng,
Zhencheng Chen
Publication year - 2019
Publication title -
the electronic journal of linear algebra
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.447
H-Index - 31
eISSN - 1537-9582
pISSN - 1081-3810
DOI - 10.13001/ela.2019.5167
Subject(s) - mathematics , positive definite matrix , eigenvalues and eigenvectors , expression (computer science) , matrix (chemical analysis) , symmetric matrix , least squares function approximation , inverse , linear least squares , algebra over a field , pure mathematics , combinatorics , singular value decomposition , algorithm , geometry , physics , materials science , statistics , quantum mechanics , estimator , computer science , composite material , programming language
In this paper, the symmetric positive semidenite Procrustes problem is considered. By using matrix inner product and matrix decomposition theory, an explicit expression of the solution is given. Based on the explicit expression given in this paper, it is easy to derive the explicit expression of the solution given by Woodgate [K.G. Woodgate. Least-squares solution of F = PG over positive semidenite symmetric P . Linear Algebra Appl., 245:171–190, 1996.] and by Liao [A.P. Liao. On the least squares problem of a matrix equation. J. Comput. Math., 17:589–594, 1999.] for the Procrustes problem in some special cases. The explicit expression given in this paper also shows that the solution of the special inverse eigenvalue problem considered by Zhang [L. Zhang. A class of inverse eigenvalue problem for symmetric nonnegative denite matrices. J. Hunan Educational Inst., 2:11–17, 1995 (in Chinese).] can be computed exactly. Examples to illustrate the correctness of the theory results are given.