Analytic functions of a matrix play a major role in the theory of differential equations. Thus, a system of ordinary differential equations with constant coefficients, written in matrix notation in the form dx/dt = AX (here, X is the column of unknown functions), has the solution x = eAtC...
is a matrix whose elements are the coefficients of the unknowns. The solution of the equations depends entirely on these numbers and on their particular arrangement. If 3 and 4 were interchanged, the solution would not be the same.
A large number of papers have studied several systems and matrix equations [14–20,3,21–24,67–69]. We often need to solve matrix equations which are shown in Table 1, where X, Y of size m × n are unknown matrices and A, B, C, D, E, F are arbitrary matrices of appropriate ...
The general coupled linear matrix equations with conjugate and transpose unknowns over the mixed groups of generalized reflexive and anti-reflexive matricesdoi:10.1007/s40314-013-0095-6Fatemeh BeikMahmoud Mohseni Moghadam
He, Z.H.: Pure PSVD approach to Sylvester-type quaternion matrix equations. Electron. J. Linear Algebra 35, 266–284 (2019) Article MathSciNet Google Scholar He, Z.H.: A system of coupled quaternion matrix equations with seven unknowns and its applications. Adv. Appl. Clifford Algebras...
where A is the n× n matrix of coefficients, x is the n× 1 column vector of unknowns, and b is the n× 1 column vector of constants. For example, suppose we had the following equations: 4x1−10x2 =−23x1+7x2 = 13 These can be written in matrix ...
With an over-determined system (3 equations and only 2 unknowns), you can't expect an exact solution. However, the solution that fsolve does find does seem to be valid as a least squares solution, judging from the surface plot below. ThemeCopy fun = @root2d; x0 = [0,0]; [x,f]...
Three equations, three unknowns. So there should be a solution, right? WRONG. x and y appear in exactly the same way in all equations. So suppose a solution (x0, y0) exists, that is the optimal solution? Then it must be true that (x0+k,y0-k) is also a completely ...
a rectangular array (see array entry 2 sense 5) of mathematical elements (such as the coefficients (see coefficient sense 1) of simultaneous (see simultaneous sense 2) linear equations) that can be combined to form sums and products with similar arrays having an appropriate number of rows and...
This set of algebraic equations (hopefully linear) can be written as a global matrix equation for the whole domain, and well-known matrix-equation solvers can be applied to generate the simulation numbers. The nodes are chosen at the time of the discretization process, which has to be done ...