Zobrazeno 1 - 7
of 7
pro vyhledávání: '"YUJI NAKATSUKASA"'
Publikováno v:
Linear Algebra and its Applications. 594:177-192
When a projection of a symmetric or Hermitian matrix to the positive semidefinite cone is computed approximately (or to working precision on a computer), a natural question is to quantify its accuracy. A straightforward bound invoking standard eigenv
Autor:
Vanni Noferini, Yuji Nakatsukasa
Sylvester's law of inertia states that the number of positive, negative and zero eigenvalues of Hermitian matrices is preserved under congruence transformations. The same is true of generalized Hermitian definite eigenvalue problems, in which the two
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::74277c576a0d8c6982cf44f1e37e0fe2
Publikováno v:
e-Archivo. Repositorio Institucional de la Universidad Carlos III de Madrid
instname
instname
We analyze the relationship between the Jordan canonical form of products, in different orders, of k square matrices A1,.,Ak. Our results extend some classical results by H. Flanders. Motivated by a generalization of Fiedler matrices, we study permut
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e0b758de633fc3e0da19be0114415809
http://hdl.handle.net/10016/22081
http://hdl.handle.net/10016/22081
We show that the unitary factor Up in the polar decomposition of a nonsingular matrix Z=UpH is a minimizer for both ‖Log(Q⁎Z)‖and‖sym⁎(Log(Q⁎Z))‖ over the unitary matrices Q∈U(n) for any given invertible matrix Z∈Cn×n, for any unit
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d8d9205e0c18446882238485f5c1d5ab
http://arxiv.org/abs/1308.1122
http://arxiv.org/abs/1308.1122
We describe our current understanding on the phase transition phenomenon of the graph Laplacian eigenvectors constructed on a certain type of unweighted trees, which we previously observed through our numerical experiments. The eigenvalue distributio
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d112b85de53bb73cb8d77e178be278bb
http://arxiv.org/abs/1112.4526
http://arxiv.org/abs/1112.4526
Autor:
Yuji Nakatsukasa
Publikováno v:
Linear Algebra and its Applications. (5):1528-1534
The Davis–Kahan tan θ theorem bounds the tangent of the angles between an approximate and an exact invariant subspace of a Hermitian matrix. When applicable, it gives a sharper bound than the sin θ theorem. However, the tan θ theorem requires mo
Autor:
Yuji Nakatsukasa
Publikováno v:
Linear Algebra and its Applications. (1):242-248
Weyl-type eigenvalue perturbation theories are derived for Hermitian definite pencils A - λ B , in which B is positive definite. The results provide a one-to-one correspondence between the original and perturbed eigenvalues, and give a uniform pertu