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        None of the usual floating point numerical techniques available for solving the quadratic matrix equation AX 2 + BX + C = 0 with square matrices A, B, C and X , can provide an
    
      
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        The Eighth Haifa Matrix Theory Con- ference was a part of the special month in Linear Algebra, organized by the Institute for Advanced Studies in Mathematics at the Technion in
    
      
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        Leoncini presented a linear time algorithm for check- ing the nonsingularity of general tridiagonal matrices [ BIT , 36:206, 1996].. A detailed implementation of their algorithm,
    
      
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        The spae of upper triangular matries with Hilbert{Shmidt norm an be viewed as a nite dimensional analogue of the Hardy spae H2 of the unit disk when one introdues the adequate notion
    
      
        Reently, the authors established a number of inequalities involving integer powers of the Hadamard produt of two positive denite Hermitian matries.. Here these results are extended