An unusual matrix is to be generated

Posted on 2008-05-13 10:45 By kharal9 (

60)

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We have a list of random binary numbers, say, A=[1,1,0,0,1,0]. Based upon A we want to write a matrix M=[a(i,j)] of order 5x5, where each a(i,j) is a list of length(A), comprising real numbers in closed interval [0,1]. All these reals in a(i,j) are less or equal to the corresponding entry in A.

Furthermore, the matrix rows and columns have to satisfy following conditions:

1. min(a(i,r),a(i,s))=[0,0,0,0,0,0] for every i,r,s such taht r<>s.
min(a(r,j),a(s,j))=[0,0,0,0,0,0] for every i,r,s such taht r<>s.

2. max(a(i,r))=A , r=1..n, for every i.
max(a(s,j))=A , s=1..n, for every j.

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Unclear description

Comment on 2008-05-17 10:03 from Joe Riel ( Maple Rating 4

1258)

Your description of the problem is not entirely clear. Maybe you could clarify. Is the 5x5 size of the Matrix completely arbitrary (from an algorithmic standpoint)? Seems like it.

How is the left side of condition 1 to be interpreted? For example, suppose a(1,1) = [x1,...,x6] and a(1,2) = [y1,...,y6], what is min(a(1,1),a(1,2))? Do you mean [min(x1,y1),...,min(x6,y6)]?

Similarly, how is condition 2 interpreted? Why not post Maple code that validates the conditions; that would clarify things and writing that code should be considerably easier than generating an algorithm to meet them. Also, you might demonstrate a Matrix that meets your requirements for a simpler case, say A = [0,1] and M a 2x2 matrix.