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Here is another way to accomplish what is in the OP's self-answer: evecRand = Sqrt[eval]*RandomVariate[NormalDistribution[], Length@evec]*evec; Appendix Test data: {eval, evec} = Eigensystem[# . Transpose[#] &@RandomReal[1, {101, 101}]];


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In the end, I have been able to write evecRand = 0*ConstantArray[1, {longitudeOfEigA}]; For[i = 0, i < realizationNumber, i++, For[j = 0, j < longitudeOfEigA, j++; evecRand[[j]] = eval[[j]]^0.5*RandomVariate[NormalDistribution[]]*evec[[j]]]]; This somehow provides me with what I want, a matrix of size 101*101.


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