The Rank of a Matrix, the Value of a Determinant, and the Solution of a System of Linear EquationsFirst page of articledoi:10.1002/sapm1932111146RiceLepine HallJournal of Mathematics & Physics
1.By using the Euclidean algorithm and invertible linear transformation over an integral ring, the solution of integral indeterminate equations of the first degree was investigated in theory, and itsmatrix solutionbased on the elementary matrix transformation was proposed.用欧几里德算法和整数环上的可逆...
-path; the latter can be obtained efficiently by a combination of a parametric pivoting-like scheme supplemented by an algorithm that takes advantage of the z-matrix structure of the loss function. similar content being viewed by others linear-step solvability of some folded concave and singly-par...
The solution is characterized by the matrix Riccati differential equation with the solution implicitly depending on mu. Approximations are utilized to explicity reveal the dependence of the Riccati solution on mu. Lower and upper bound of the solution for all mu of interest are derived and a ...
The numerical solution produced bysol = pdepe(m,@pdefun,@pdeic,@pdebc,xmesh,tspan)uses the coordinate symmetrymand spatial meshxmeshto return a 3-D matrix of the solution valuessol. Reuse themandxmeshinputs used to calculate the solution when you callpdeval. ...
SolutionoftheMatrixEquationAX-XB=C.Inthispaperafinitealgebraicformulaforthesolutionof thematrixequationAX-XB=Cisderived.Basedonit,anewdirectalgorithmisgiven. AMSSubjectClassification:65F10. Keywords:Matrixequation,algebraicformula. LiisnngderMatrixgleiehungAX-XB=C.AngegebenwirdeinealgebraischeFormelfiirdieL6...
【解析】 译文:已知方程组$$\left\{ \begin{matrix} 3 x + 2 y = a \\ 2 x + 3 y = 2 \end{matrix} \right.$$的解是一个正数和一个负数,则a的取值范 围是( ) (A) (B) $$ ( A ) \frac { 4 } { 3 } 3 $$(D)$$ a > 3 $$或$$ a 0 , y 0 \\ \frac { 6 - 2...
The solution is a 51-by-1-by-51 array. Usesqueezeto remove the singleton dimension. Removing the singleton dimension transforms this array to a 51-by-51 matrix which simplifies indexing into it. uintrp = squeeze(uintrp); Plot the solution as a function ofyand time. ...
positive definite solutionIn this note, we argue that Theorem 2.2 and its proof in Duan XF, et al. is seriously flawed and prove a new result based on Brouwer’s fixed-point theorem.Keywords: nonlinear matrix equation, stochastic control, positive definite solution, AMS Subject ...
The purpose of this paper is to study the existence and uniqueness of a positive definite solution to the nonlinear matrix equation X = Q − A∗X −1A + B∗X −1B, which is a special stochastic rational Riccati equation arising in stochastic control theory. Methods Ou...