where is the Hermitian matrix formed by deleting the row and column from . When we posted the first version of this paper, we were unaware of previous appearances of this identity in the literature; a related identity had been used by Erdos-Schlein-Yau and by myself and Van Vu for applic...
Let be a large natural number, and let be a matrix drawn from the Gaussian Unitary Ensemble (GUE), by which we mean that is a Hermitian matrix whose upper triangular entries are iid complex gaussians with mean zero and variance one, and whose diagonal entries are iid real gaussians with ...
A Hermitian matrix is diagonalizable because the eigenvectors can be taken to be mutually orthogonal. The same is true for a normal matrix (one for which ). A matrix with distinct eigenvalues is also diagonalizable. Theorem 1. If has distinct eigenvalues then it is diagonalizable. Proof.Let hav...
A Hermitian matrix is diagonalizable because the eigenvectors can be taken to be mutually orthogonal. The same is true for a normal matrix (one for which ). A matrix with distinct eigenvalues is also diagonalizable. Theorem 1. If has distinct eigenvalues then it is diagonalizable. Proof. Let ...
The 1/N expansion in quantum field theory is formulated within analgebraic framework. For a scalar field taking values in the N byN hermitian matrices, we ... HOLLANDS,STEFAN - 《Reviews in Mathematical Physics》 被引量: 12发表: 2004年 ...
zero spin particlenon-Hermitian matrixnon-zero eigenvaluesCasimir operatorthe third componentSpin Topological SpaceSTSbinding energy of spin particlesThere is no any spin rotational construction for zero spin particle, Casimir operator and the thired component of zero spin particle areandrespectively. Furthe...
SGETRS, DGETRS, CGETRS, and ZGETRS (General Matrix Multiple Right-Hand Side Solve) SPOSV, DPOSV, CPOSV, and ZPOSV (Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization and Multiple Right-Hand Side Solve) SPOTRF, DPOTRF, CPOTRF, and ZPOTRF (Positive Definite Real Sym...
Matrix is CSR 3-array-variation 1-based (Upper triangle part of hermitian matrix) with about 22 000 000 nonzeros and 64000x64000 size The same program with smaller size worked, max size tested 17280x17280. The program executed on the: MACHTYPE=x86_64-suse-linux; HP DL580 G5 with 4x...
where κ is the condition number, and ϵ is the target accuracy.” According to the authors, their “method is applicable to general non-Hermitian matrices, and the cost, as well as the number of qubits, can be reduced when restricted to Hermitian matrices, and further to Hermitian posi...
Recall that an Hermitian matrix is said to have simple eigenvalues if all of its eigenvalues are distinct. This is a very typical property of matrices to have: for instance, as discussed in this previous post, in the space of all Hermitian matrices, the space of matrices without all ...