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LaTeX'ed the question, improved formatting a bit
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edit approved May 31, 2016 at 13:43
Rodrigo de Azevedo
edit approved May 31, 2016 at 13:43
Rodrigo de Azevedo
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Suppose we have an n by m$n \times m$ nonnegative matrix A$A$, where each row sums to 1$1$. I wonder whether there exists an m by n$m \times n$ nonnegative matrix X$X$ that satisfies the following constraints: each row of X sums to 1; the diagonal entries of matrix AX are all equal and they are lager or equal to any other entries of the matrix.

  • each row of $X$ sums to $1$.
  • the diagonal entries of matrix $AX$ are all equal and they are larger or equal to any other entries of the matrix.

If the solution does not always exist, would be interesting to know iffnecessary and sufficient conditions for such a solution to exist.

There are existence and uniqueness results for linear equations here and there, but this problem is about existence of a matrix with some particular constraints. Has been a while and still have no clue how to attack it.

Suppose we have an n by m nonnegative matrix A, where each row sums to 1. I wonder whether there exists an m by n nonnegative matrix X that satisfies the following constraints: each row of X sums to 1; the diagonal entries of matrix AX are all equal and they are lager or equal to any other entries of the matrix.

If the solution does not always exist, would be interesting to know iff conditions for such a solution to exist.

There are existence and uniqueness results for linear equations here and there, but this problem is about existence of a matrix with some particular constraints. Has been a while and still have no clue how to attack it.

Suppose we have an $n \times m$ nonnegative matrix $A$, where each row sums to $1$. I wonder whether there exists an $m \times n$ nonnegative matrix $X$ that satisfies the following constraints:

  • each row of $X$ sums to $1$.
  • the diagonal entries of matrix $AX$ are all equal and they are larger or equal to any other entries of the matrix.

If the solution does not always exist, would be interesting to know necessary and sufficient conditions for such a solution to exist.

There are existence and uniqueness results for linear equations here and there, but this problem is about existence of a matrix with some particular constraints. Has been a while and still have no clue how to attack it.

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Ann
Ann
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Suppose we have an n by m nonnegative matrix A, where each row sums to 1. I wonder whether there exists an m by n nonnegative matrix X that satisfies the following constraints: each row of X sums to 1; the diagonal entries of matrix AX are all equal and they are lager or equal to any other entries of the matrix.

If the solution does not always exist, would likebe interesting to know iff conditions for such a solution to exist.

There are existence and uniqueness results for linear equations here and there, but mythis problem is theabout existence of a matrix with some particular constraints. Has been a while and still have no clue how to attack it.

Suppose we have an n by m nonnegative matrix A, where each row sums to 1. I wonder whether there exists an m by n nonnegative matrix X that satisfies the following constraints: each row of X sums to 1; the diagonal entries of matrix AX are all equal and they are lager or equal to any other entries of the matrix.

If the solution does not always exist, would like to know iff conditions for such a solution to exist.

There are existence and uniqueness results for linear equations here and there, but my problem is the existence of a matrix with some particular constraints. Has been a while and still have no clue how to attack it.

Suppose we have an n by m nonnegative matrix A, where each row sums to 1. I wonder whether there exists an m by n nonnegative matrix X that satisfies the following constraints: each row of X sums to 1; the diagonal entries of matrix AX are all equal and they are lager or equal to any other entries of the matrix.

If the solution does not always exist, would be interesting to know iff conditions for such a solution to exist.

There are existence and uniqueness results for linear equations here and there, but this problem is about existence of a matrix with some particular constraints. Has been a while and still have no clue how to attack it.

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Ann
Ann
  • 49
  • 4

Existence of Nonnegative Solutions of Linear Systems of Equations and Inequalities with particular constraints

Suppose we have an n by m nonnegative matrix A, where each row sums to 1. I wonder whether there exists an m by n nonnegative matrix X that satisfies the following constraints: each row of X sums to 1; the diagonal entries of matrix AX are all equal and they are lager or equal to any other entries of the matrix.

If the solution does not always exist, would like to know iff conditions for such a solution to exist.

There are existence and uniqueness results for linear equations here and there, but my problem is the existence of a matrix with some particular constraints. Has been a while and still have no clue how to attack it.