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Matrix problems

  1. Oct 11, 2008 #1
    1. The problem statement, all variables and given/known data
    1)Find all matrices X that satisfy the equation A*X*B^T = C, in terms of the LU
    factorizations of A and B. State the precise conditions under which there are no
    solutions.

    B^T is the transpose of B.

    2) Let U_1 and U_2 be two upper-triangular matrices. Let Z be an m × n matrix. Let
    X be an unknown matrix that satisfies the equation
    U_1X + XU_2 = Z.
    A. Give an algorithm to find X in O(mn(m+ n)) flops (floating-point operations).
    B. Find conditions on U_1 and U_2 which guarantee the existence of a unique solution
    X.
    C. Give a non-trivial example (U_1 is not equal to 0, U_2 is not equal to 0, X is not equal to 0) where those conditions are
    not satisfied and
    U_1X + XU_2 = 0.


    2. Relevant equations



    3. The attempt at a solution
    any hints?
     
  2. jcsd
  3. Oct 11, 2008 #2
    anyone has any hints? how should i attempt these problems?
     
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