Matrixequation,algebraicformula.LiisnngderMatrixgleiehungAX-XB=C.AngegebenwirdeinealgebraischeFormelfiirdieL6sungderGleichungAX-XB=CundeinaufihrbasierenderL6sungsalgorithmus.1.IntroductionWeconsiderthematrixequationAX-XB=C(1)whereA,B,Careknownmxm,nxnandrnxnmatricesrespectively.Asiswellknown,thereisaunique...
conjugate-normal matrixunitary similarityunitary congruencenumerical algorithmsThe matrix equation AX + XB = C , where XB is obtained by the entry-wise conjugation of X , is examined. On the basis of analogy with the Sylvester matrix equation, special cases are distinguished where the former ...
参考文献 [1] H. Flanders and H.K. Wimmer, On the matrix equation AX-XB=C and AX-YB =C, SIAM J. Appl. Math., 32(1977),707-710.
摘要: A necessary and sufficient condition for the existence of expression of general solution of the matrix equation AXB+CXD=E over a skew field are given. A practical method of solving the equaiton is also presented.关键词: Corpus Solution of equation Necessary and sufficient conditions 被引...
Matrix equation AXB = Creproductive equationreproductive solutionIn this paper we represent a new form of condition for the consistency of the matrix equation AXB = C . If the matrix equation AXB = C is consistent, we determine a form of general solution which contains both reproductive and ...
A necessary and sufficient condition for the matrix equation AXB+ CYD= E to be consistent is established, and if it is, a representation of the general solution is given, thus generalizing earlier results concerning the equation AX+ YB= C....
The positive definite solutions of the matrix equation X-A*X-αA-B*X-βB=I,α,β∈(0,1] were investigated.Necessary and sufficient conditions for the existence of positive definite solutions were derived,which generalize the existing related results.A necessary condition for the existence of th...
Multiply xx by each element of the matrix. [x⋅1x⋅−1]+y[21]=[ab][x⋅1x⋅-1]+y[21]=[ab] Step 1.2 Simplify each element in the matrix. Tap for more steps... Step 1.2.1 Multiply xx by 11. [xx⋅−1]+y[21]=[ab][xx⋅-1]+y[21]=[ab] Step 1.2.2 Move ...
The solution of the matrix equation AXB=D and the system of matrix equations AX=C,XB=D with X*X=I<inf>p</inf> 2022, Applied Mathematics and Computation Show abstract A survey of distributed algorithms for solving matrix equations 2021, Kongzhi Lilun Yu Yingyong/Control Theory and Applicatio...
The sensitivity of the solution X to the matrix equation AX - XB = C is primarily dependent on the quantity sep (A, B) introduced by Stewart (1973) in conn... JM Varah - 《Siam Journal on Numerical Analysis》 被引量: 140发表: 1979年 The Sensitivity of the Stable Lyapunov Equation An...