denotes the complex conjugate transpose of A. We write (), if matrix A is positive definite (positive semidefinite). If is positive definite (positive semidefinite), then we write (). Moreover, we denote by the spectral radius of A. We use and to denote the maximal and minimal eigenvalues...
When F=AH (the conjugate transpose of A), the matrix equations are the well-known Lyapunov equation and Stein equation (or, discrete-time Lyapunov equation), respectively. There exist several numerical algorithms to compute the solutions of the above matrix equations such as the Bartels–Stewart ...
CGEMV and ZGEMV compute the matrix-vector product for either a complex general matrix, its transpose, or its conjugate transpose, using the scalarsαandβ, vectorsxandy, and matrixA, its transpose, or its conjugate transpose: y←βy+αAx...
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 uppertriangularR so thatR'*R = X. If X is not ...
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, ...
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...
z* complex conjugate z = a+bi→ z*=a-bi z* = 3 - 2i z complex conjugate z = a+bi→ z = a-bi z = 3 - 2i Re(z) real part of a complex number z = a+bi→ Re(z)=a Re(3 - 2i) = 3 Im(z) imaginary part of a complex number z = a+bi→ Im(z)=b Im(3 - ...
clementpoiret Some more details: If I wrap x aroundQuantStubandDeQuantStubas in PyTorch's doc, such as: # Define your main model hereclassVeryComplexModel(nn.Module):def__init__(self):super().__init__()self.quant=QuantStub()self.dequant=DeQuantStub()self.backbone=timm.create_model("...
In step 4, the superscript symbol ΓΓ is the conjugate transpose of the tensor, k is the number of training datasets, and 𝜂η is the variation coefficient of the iterative solution model. In step 5, ∇𝑓∇f is the gradient defined in the tensor space. In step 6, 𝑃𝑟𝑜...