If A is the b à b matrix with entries denoted as aij i = 1,...,b, j = 1,...,b, B = diag(A) is the ... Define b(x) as some real valued function such that b/(x) and b//(x) are the 1st and 2nd derivative ... This operation performs element-wise multiplication of.
S1 Text Some matrix notation used in text. Below we list some notation and distribution theory used in the main part of the text. A) is the If A is the b × b matrix with entries denoted as aij i = 1, . . . , b, j = 1, . . . , b, B = diag(A diagonal matrix with diagonal elements bii = aii and off-diagonal elements all equal to zero. The A) denotes the b × 1 vector containing the diagonal elements of the matrix A . identity diagonal(A The trace of a matrix is defined as the sum of the diagonal elements of a matrix such that P A) = i aii . tr(A The transpose of the matrix A is denoted as A T . Define b(x) as some real valued function such that b0 (x) and b00 (x) are the 1st and 2nd derivative of b(x) respectively. Let l be a column vector such that b (ll ) is a column vector where the ith element is b(li ). A B denotes the Hadamard product. This operation performs element-wise multiplication of the elements in A and B where A and B are conformable matrices. µ Σ ) then for some matrix Γ , E(X X T ΓX ) = tr (Γ ΓΣ ) + µ T Γµ . The entropy of the If X p ∼ N (µ R x) ln f (x x)dx x = − p2 (ln(2π) + 1) − 12 log |Σ Σ|. Gaussian distribution is defined as f (x
