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The distance matrix of G, denoted by (D(G)), is the symmetric real matrix with ((i, j))-entry being (d_{ij}).
Let Δ(M) denote the diagonal matrix with i th diagonal entry [Δ(M ] ii = M ii, where [P] ab denotes the entry (a, b) of matrix P.
For industry sector i belonging to the group of primary industries (i.e., i ∈ primary industry ), we define S a to be the ( N × N ) diagonal matrix with i th diagonal element equal to 1 and all other elements equal to 0. Here, the subscript a indicates primary industries (i.e., agriculture, forestry, and fishery industries).
where R and t are the rotation and translation matrix, respectively, (z^{X}_{i,j}) is the depth of the model point cloud, and (z^{Y R,t)}_{i,j}) is the depth of the data point cloud after applying the rotation and translation matrix with i,j from the ray casting process.
For the case of random matrix with i.i.d.i.d
W t is the K×N2 data matrix with i.i.d.i.d
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For example, the SNP BFs of NBF can be computed as (11) where equals the genotype matrix with its i th column (i.e. the contribution of the i th SNP) removed.
Here, G W ( n ) Open image in new window is a diagonal matrix with its i th element equal to G w i ( n ) Open image in new window.
Further denote by I the identity matrix and by diag(v ) a diagonal matrix with its i-th diagonal component given by v i 2, i = 1,..., n.
For each t ∈ I, let B i ( t ) be a positive semidefinite n × n matrix with B i continuous on I, i = 1, 2, …, p and the symbol T denotes the transposition.
Random matrices with i.i.d.i.d
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com