Let // denote Hadamard element-wise division.
where ∗ denotes the Hadamard (element-wise) matrix product.
where ⊙ denotes Hadamard (element-wise) product of matrices, and U 0,0=I.
The symbol denotes the Kronecker (or direct) product of two matrices, and denotes their Hadamard (component-wise) product.
We use the symbol and to denote the Hadamard (element-wise) product and Kronecker product between matrices, respectively.
Addition and multiplication of diagonal matrices (mathop {mathrm {diag}}(a_0, a_1, ldots )) corresponds to the usual addition and the Hadamard (coefficient-wise) multiplication of the power series (a_0+a_1s+a_2s^2+cdots ).
We then use O to further improve the reconstructed foreground ( widehat{mathbf{F}} ) through ( odot kern0.5em widehat{mathbf{F}} ), where ⊙ denotes the Hadamard (point-wise) product.
where ∘ denotes the Hadamard (element wise) product, diagonal positive definite matrices for thermal conductivity and volumetric heat capacity M k, M ρ c, discrete divergence and gradient operators S ˜, − S ˜ ⊤ on the dual grid, respectively.
Here, n' is a random integer perturbation, ⊙ is the Hadamard (element-wise) product, and the l th column of the displacement matrix D k is given by el+d(l), with the canonical column unit vector [ e l ] n = 1, l = n, 0, else, and a random integer jitter d(l) whose probability mass is concentrated about zero.
We can form a row vector of these products for each column by taking the Hadamard (element-wise) product of rows Wi ra,) and Wj rb,).
Then the variance of the score statistic can be expressed as where ○ denotes the (Hadamard) term-wise product.
