Sentence examples for matrix determinants from inspiring English sources

Based on the characteristic polynomial of the symbolic force-density matrix, the two threee) lower-order coefficients that are necessary for the form-finding of planar (three-dimensional) tensegrities are expressed by a unified compact equation using the matrix determinants.

The constrained maximization problem is expressed as the fraction of matrix determinants, and a sequential convex programming algorithm is adopted for the solution of the corresponding non-convex problem.

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).

Random nested terms are usually not applicable in a MANCOVA framework (i.e., matrix determinants can become negative, making the term untestable, and type I error rates may be inflated when nested terms in MANCOVA models are significant; see Rencher 2002, p. 162; and Langerhans and Makowicz 2009).

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.

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

where |.| denotes the matrix determinant operator.

Calculating the matrix determinant in (14) requires a complexity of.

The matrix determinant has an order of complexity of.