In this paper we make a complete perturbation analysis of the nonlinear matrix equation, where A and B are square complex matrices, denotes the complex conjugate transpose of the matrix A and I is the identity matrix. We obtain local (first order) perturbation bounds and a non-local ...
The chol function uses only the diagonal and upper triangle of X. The lower triangular is assumed to be the (complex conjugate) transpose of the upper. That is, X is Hermitian. R = chol(X), where X is positive definite produces an upper triangular R so thatR'*R = X. If X is not...
CGEMV and ZGEMV compute the matrix-vector product for either a complex general matrix, its transpose, or its conjugate transpose, using the scalars α and β, vectors x and y, and matrix A, its transpose, or its conjugate transpose: ...
Computes the solution to the system of linear equations with a square coefficient matrix A and multiple right-hand sides, and provides error bounds on the solution.
The man page routine names use lowercase letters. For many routines, separate routines exist that operate on different data types. Rather than list each routine separately, a lowercase x is used in a routine name to denote single, double, complex, and double complex data types. For example, ...
complex_check <- function(qstate_obj) { return(qstate_obj@coefs |> class() ) } 22 changes: 22 additions & 0 deletions 22 R/conjugate_transpose.R Original file line numberDiff line numberDiff line change @@ -0,0 +1,22 @@ #' Calculate the Conjugate Transpose of a Quantum State ...
Perturbation analysis of the Hermitian positive definite solution of the matrix equation XA*X2A=I - ScienceDirect Consider the nonlinear matrix equation X A * X 2 A = I , where A is an n × n complex matrix, I the identity matrix and A * the conjugate transpose of... M Cheng,S ...
Consider the nonlinear matrix equation X-A~*X~(-1)A=Q,where A,Q are n×n complex matrices with Q Hermitian positive definite and A~* denotes the conjugate transpose of a matrix A.This paper shows there exists a unique positive definite solution to the equation. The perturbation bounds for...
adjoint_function: XDiag requires multiplications with bothAand its (conjugate) transposeA'. IfAis specified by a function handle, then this optional argument allows the user to specify a function handle which computes the action of the adjoint of the matrix@(X) A'*X. If this argument is not...
In addition, the matrix equation X−AX¯F=C is also studied. An explicit solution for this matrix equation is also proposed by means of the real representation of a complex matrix. This solution is neatly expressed by a symmetric operator matrix, two controllability matrices and two ...