The product (oplus) indicates entry-wise multiplications.
and the matrices and are entry-wise defined by (2.15).
For example, it can be an entry-wise closeness of UV to X or alternatively the closeness at the individual spectra.
Let A be an irreducible nonnegative n × n matrix and B be a complex n × n matrix such that | B | ≤ A (entry-wise).
where the symbol "°" represents the Hadamard product, which is known as entry-wise multiplication [33], while M θ is the masking matrix at rotation angle θ.
We propose a convex variational approach to compute localized density matrices for both zero temperature and finite temperature cases, by adding an entry-wise ℓ1 regularization to the free energy of the quantum system.
For two matrices A and B, denote by A ⊙ B the entry-wise multiplication of A and B, that is, the matrix whose entries are a i,j b i,j.
Throughout the article, ⊤ denotes the matrix transpose, H the Hermitian transpose, ¯ the entry-wise complex conjugate of a matrix, and by Gl(m) the set of all m×m invertible complex matrices.
where the entries of the vector functions λ0, λ s, λx 1, λx 2, λ p are SOS, the vector functions g0, g s, gx 1, gx 2, g p satisfy g* ≥ 0 (entry-wise) whenever x∈X* or p∈Par, respectively, and we assume |Q| = 1 for notational convenience.
Let us recursively define the matrices αt,t=I K (where I K denotes the identity matrix) and αs,t, constructed entry-wise as (alpha _{s,t}^{ij} = sum _{k=1}^{K} alpha _{s+1,t}^{ik} alpha _{s}^{kj}), for i,j∈{1,...,K} and 0≤s
