Although there is no 3-dimensional analogue of the complex numbers, the relationship between the positions of the centers can be re-expressed as a matrix equation, which also generalizes to dimensions.
32.
Consequently, the input voltage / current matrix vector can be directly replaced with the matrix equation of the preceding cascaded stage to form a combined \ scriptstyle A'B'C'D'matrix.
33.
He has more than 85 refereed publications on topics such as rounding error analysis, linear systems, least squares problems, matrix functions and nonlinear matrix equations, condition number estimation, and generalized eigenvalue problems.
34.
Therefore, the task of converting the image back into the intended domain involves solving an underdetermined matrix equation since the number of compressive measurements taken is smaller than the number of pixels in the full image.
35.
It attempts to approximate the solution to some equation by piecewise linear functions, where the pieces are chosen with respect to a sufficiently fine grid, which in turn can be recast as a matrix equation.
36.
When this vector of final demand is multiplied by the Leontief inverse, we obtain total output . is the identity matrix so that the following matrix equation is the result of equivalence operations in our previous equation:
37.
This matrix equation is very simple to implement and requires only that the 3D FT of the basis functions be computed, preferably in closed form ( see Scott [ 1998 ], available on researchgate . net ).
38.
In contrast, as Craymer explains, it is also possible to perform a full simultaneous or in-context least-squares fit by solving a matrix equation, partitioning the total data variance between the specified sinusoid frequencies.
39.
Remarkably, while the forward kinematics of a serial chain is a direct calculation of a single matrix equation, the forward kinematics of a parallel chain requires the simultaneous solution of multiple matrix equations which presents a significant challenge.
40.
Remarkably, while the forward kinematics of a serial chain is a direct calculation of a single matrix equation, the forward kinematics of a parallel chain requires the simultaneous solution of multiple matrix equations which presents a significant challenge.
