where |·| is the matrix determinant and D k the number of parameters in θ k.
Drury et al. [1] introduced the matrix, determinant and trace version of the Wielandt inequality.
Matrix, determinant, and trace versions of it have been presented in the literature.
The superscripts * stands for complex conjugate and det and |·| refer the matrix determinant and absolute value in that order.
where Det denotes the matrix determinant and K y ( i ) = E y ( i ) ( y ( i ) ) H = G ( i ) K h ( i ) ( G ( i ) ) H + σ i 2 I. Next, we show the term ∏ i = 1 M Det K y ( i ) is independent of (x, y).
For the one-variance component model, the permutations can be done extremely cheaply by caching all the expensive computations from the real data (computations related to the matrix determinant and inverse), thereby reducing the computational complexity from quadratic to linear in the size of the gene sets.
Many matrix consistency testing methods were developed, such as matrix determinant (Pelaez and Lamata 2003), ratio of calculated priorities and given comparison (Grawford and Williams 1985), transitivity rule (Salo and Hamalainen 1997; Ji and Jiang 2003), and normalized column of the comparison matrix (Stein and Mizzi 2007).
where E denotes the statistical expectation operator, det is the matrix determinant operator, and K is the number of frequency bins.
The expression, given in terms of matrix determinants, is compacter in representation and more efficient in computational complexity than existing results in the literature.
Derivatives of galactose in glycoconjugates are key elements of cell membrane structures, hormones, extracellular matrix, immunologic determinants and structural elements of the central nervous system, among other roles (Segal, 1995).
