Mixing
Existence of a probability vector solution
$begingroup$
I have a linear system Ax = b where A and b are nonnegative and the columns of A sum up to one and the vector b also sums up to one. The matrix A can be assumed to be fat (more columns than rows).
Under what conditions on A is it true that there exists a probability vector x (a nonnegative vector whose components sum up to one) for any b?
Thanks,
Vincent
linear-algebra
asked Jan 24 at 1:06
Vincent TanVincent Tan
11
$endgroup$
add a comment |
$begingroup$
I have a linear system Ax = b where A and b are nonnegative and the columns of A sum up to one and the vector b also sums up to one. The matrix A can be assumed to be fat (more columns than rows).
Under what conditions on A is it true that there exists a probability vector x (a nonnegative vector whose components sum up to one) for any b?
Thanks,
Vincent
linear-algebra
asked Jan 24 at 1:06
Vincent TanVincent Tan
11
$endgroup$
add a comment |
$begingroup$
I have a linear system Ax = b where A and b are nonnegative and the columns of A sum up to one and the vector b also sums up to one. The matrix A can be assumed to be fat (more columns than rows).
Under what conditions on A is it true that there exists a probability vector x (a nonnegative vector whose components sum up to one) for any b?
Thanks,
Vincent
linear-algebra
asked Jan 24 at 1:06
Vincent TanVincent Tan
11
$endgroup$
I have a linear system Ax = b where A and b are nonnegative and the columns of A sum up to one and the vector b also sums up to one. The matrix A can be assumed to be fat (more columns than rows).
Under what conditions on A is it true that there exists a probability vector x (a nonnegative vector whose components sum up to one) for any b?
Thanks,
Vincent
linear-algebra
linear-algebra
asked Jan 24 at 1:06
Vincent TanVincent Tan
11
asked Jan 24 at 1:06
Vincent TanVincent Tan
11
asked Jan 24 at 1:06
Vincent TanVincent Tan
11
asked Jan 24 at 1:06
Vincent TanVincent Tan
11
asked Jan 24 at 1:06
Vincent TanVincent Tan
11
11
add a comment |
add a comment |
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