how can i compute the interior of a vector product of two sets.

W is a subset of int BU------ condition 1

BU--- Image of U with respect to the linear mapping associated to the matrix B

w is known

B is known

i want to compute U such that condition 1 is met.

[Azzi Abdelmalek]

What is the interior of a vector ?

[Jeffrey Eiyike]

B is a matrix not a vector... Sorry i use a wrong title. Check the body i explained it properly.

[John D'Errico]

You MAY have explained it properly in your opinion, but you hardly explained it clearly.

B is a matrix. Is B a square matrix? Is B singular? What do you know about B that you are not telling us?

From your comments, one assumes that this is a linear algebra problem. U is a column vector of length n, corresponding to a matrix B of size m by n.

You say that W is a subset of int BU. Does int here refer to an integral? Or are you taking the integer part of the elements of (B*U)? What is W a subset of?

Is W the same as w? I presume that must be, since you don't seem to reference either variable more than once.

What do you mean when you refer to the interior of the set? And how do you expect it to be represented in MATLAB?

Be clear!

[Jeffrey Eiyike]

not just a subset but a proper subset.. B is not a square matrix its a 7x9 matrix.... int means interior.....

BU means image of U with respect to the linear mapping associated to the matrix B..

[Steven Lord]

It's still not clear exactly what you're trying to do. Please show a (small) concrete example. Post the code that creates B and w (in a form that people reading the question can run; no dependency on other functions or data files unless you post the data.) Then post the exact U that you want to compute and explain as best you can why that U is the correct answer. to the problem you're trying to solve.

[Jeffrey Eiyike]

This paper discuss something close to what i want....How do i upload my code? That matrix is B

How do i upload it. I have over 7 function files and the main code..

     1     0     0    -1     0     0     0     0     0;
     0     1     0     0    -1     0     0     0     0;
     0     0     1     0     0    -1     0     0     0;
     1     1     0     0     0     0    -1     0     0;
     1     0     1     0     0     0     0    -1     0;
     0     1     1     0     0     0     0     0    -1;
     1     1     1     0     0     0     0     0     0;

[John D'Errico]

Why do I feel as if we have been forced to drag information out of you like we are pulling teeth? Is the matrix B full rank or not???????? Is it really that difficult to answer questions?

I'll assume that W is a 7xM array, where each column of W is one member of the set of interest. So the vectors in W span some subspace of R^7. I'm guessing that you wish to identify the set of vectors U that will map into the subspace spanned by the columns of W? Essentially, it looks like you are asking for the span of the image of W through the linear mapping B, an inverse image?

The point being, if B is of less than full rank, then it seems we would need to consider the nullspace of B. I'm still guessing at the problem statement though.

[Steven Lord]

Please do NOT send me your code via email. Post a SMALL example here so everyone who reads this question can read and potentially contribute to the answer.

[Jeffrey Eiyike]

Let me cite an example... here..

w_upper= [7 10.5 13 28 28 28 40.5] % 7x1

w_upper=[-7 -4 -1 21.5 21.5 21.5 34.9110] % 7x1

B is the initial Matrix i posted. 7 by 9 matrix

**W is a proper subset of interior of ( the image of U with respect to linear mapping associated with matrix B.

xdot=Bu(t)-Ew(t)

u is a 9x1

E is an identity matrix.

x is a 7x1

BU is the image of U with respect to the linear mapping associated to the matrix B.

While select the upper and lower limit the condition in the picture must be met..

All i want to achieve is an upper and lower limit for u(t) such that the condition *** is met. Also if u and w has a upper and lower limit then x should also have a limit..

Am sorry for the inconvinience.. thats the example...

[Jeffrey Eiyike]

@John, A={the image of U through a linear mapping B}.

*And W

w_upper= [7 10.5 13 28 28 28 40.5] % 7x1

w_lower=[-7 -4 -1 21.5 21.5 21.5 34.9110] % 7x1

should be a subset of the interior A stated above.. So the upper and lower bound of u should satisfy the condition ***

xdot= Bu - W

x should also have an upper and lower limit