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This paper investigates the uniqueness of a nonnegative vector solution and the uniqueness of a positive semidefinite matrix solution to underdetermined linear systems. A vector solution is the unique solution to an underdetermined linear system only if the measurement matrix has a row-span intersecting the positive orthant. Focusing on two types of binary measurement matrices, Bernoulli 0-1 matrices...
This paper investigates conditions for an underdetermined linear system to have a unique nonnegative solution. A necessary condition is derived which requires the measurement matrix to have a row-span intersecting the positive orthant. For systems that satisfy this necessary condition, we provide equivalent characterizations for having a unique nonnegative solution. These conditions generalize existing...
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