代码很简单，
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ranOrt := Orthogonalize[RandomInteger[4, {4, 4}]] ranOrt // MatrixForm P = ranOrt; P.Transpose[P] // Simplify // MatrixForm |
非整数的
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ranOrt := Orthogonalize[RandomVariate[NormalDistribution[], {4, 4}]] ranOrt // MatrixForm P = ranOrt; P.Transpose[P] // Simplify // MatrixForm |