Abstract
The purpose of this paper is to characterize and interrelate various degrees of stability and semipositivity for real square matrices having nonpositive off-diagonal entries. The major classes considered are the sets of diagonally stable, stable, and semipositive matrices, denoted respectively by A , L , and S . The conditions defining these classes are weakened, and the resulting classes are examined. Their relationship to the classes of real matrices P and P 0, whose off-diagonal entries are nonpositive and whose principal minors are respectively all positive and all nonnegative, is also included.
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