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The matrix equation XA + AX T = 0, which has relevance to the study of Lie algebras, was recently studied by De Terán and Dopico (Linear Algebra Appl. 434 (2011), 44–67). They reduced the study of this equation to several special cases and produced explicit solutions in most instances. In this note we obtain an explicit solution in one of the difficult(More)
The matrix equation XA + AX T = 0 was recently introduced by De Terán and Dopico (Linear Algebra Appl. 434 (2011), 44–67) to study the dimension of congruence orbits. They reduced the study of this equation to a number of special cases, several of which have not been explicitly solved. In this note we obtain an explicit, closed-form solution in the(More)
The probabilistic method is one of the most significant contributions of Paul Erd˝ os. Indeed, Paul himself said, during his eightieth birthday conference in Keszthely, Hungary, that he believes the method will live long after him. This was the only time I heard him making any comment about the significance and impact of his work. He was always more(More)
The matrix equation XA + AX T = 0, which has relevance to the study of Lie algebras, was recently studied by De Terán and Dopico (Linear Algebra Appl. 434 (2011), 44–67). They reduced the study of this equation to several special cases and produced explicit solutions in most instances. In this note we obtain an explicit solution in one of the difficult(More)
Previous methods for measurement of the autokinetic effect have several drawbacks, including limited accuracy and limited information. A new computer technique for measurement of the autokinetic effect is presented. A computer and computer mouse record tracing movements every tenth of a second, yielding a permanent record that can be analyzed further. The(More)
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