Sentence examples for matrix determinants is from inspiring English sources

The expression, given in terms of matrix determinants, is compacter in representation and more efficient in computational complexity than existing results in the literature.

However, the expression given in Eq. 20 is not in a convenient form for auxiliary channel selection; a concise formula in terms of matrix determinants is derived as follows: The middle term in Eq. 20 is denoted with G T and is expressed as: {mathbf{G}_{T}} = mathbf{V}_{T}^{H}{mathbf{V}_{T}} + {mathbf{Phi }_{I}} (21).

Reciprocal results based on Grassmann geometry are categorized, and used for analyzing surfaces whose Jacobian matrix determinant is zero.

Stiffness matrix determinant is an algebraic sum including n! terms each of which is the product of n factors belonging to different rows and columns.

In order to perform this analysis, the sensitivity coefficients and the sensitivity matrix determinant were examined.

In order to perform this analysis, the sensitivity coefficients and the sensitivity matrix determinant were calculated.

The correlation matrix determinant was checked for indications of multicollinearity (should be >0.00001) and the Kaiser-Meyer-Olkin statistics (KMO) for sampling adequacy (should be >0.5 for individual variables and >0.7 for overall KMO) [ 8].

For the case where precisely one of the two variance components is full rank (has more SNPs than individuals, as might happen when correcting for family-relatedness and population structure), we have developed a new approach for the LR test in which expensive computations (matrix inverses and determinants) are replaced by cheaper low-rank-update versions of them.

Tr(A) is the trace of A, while A F 2 denotes the squared Frobenius norm of A. For a square matrix A, |A| is the matrix determinant, A-1 is the matrix inverse, and A-1/2 is the matrix inverse square root.

Accordingly, (mathbf {I}_{N}+frac {P}{sigma ^{2}}mathbb {E}left [mathbf {H}mathbf {S}mathbf {H}^right ]) is also a diagonal matrix, and its determinant is the product of its diagonal elements.

For simplicity, we assume Σ k is a diagonal matrix and its determinant is ({sigma ^{2}_{m}}), which is calculated as the mean of the square distances between the the mean vectors of the Gaussian model and their five nearest neighbors as follows: {sigma^{2}_{m}}= sum_{mathbf{x}_{i} in text{NN}_{5}({mu}_{m})} | mathbf{x}_{i}- {mu}_{m} |^{2}, (3).