It is shown that in solving for the symmetric matrixPthe number of linear equations and unknowns can be reduced from1/2n(n + 1)to1/2n(n - 1)by introducing a skew-symmetric matrix. This corresponds to an earlier result for the equationA₁TP₁ + P₁A = -Q.
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Stephen M. Barnett (1974) studied this question.
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