Dear all, my question is not directly related to R, however I believe that
experts here would not mind anything to have a look on my problem.

Please consider a symmetric matrix and it's eigen values:

> set.seed(1)
> mat <- matrix(rnorm(36), 6)
> mat <- mat %*% t(mat) # symmetric matrix
> mat
          [,1]       [,2]        [,3]       [,4]       [,5]        [,6]
[1,]  3.920570  1.9339770  1.29012167 -1.4627174 -1.5655953 -1.82083435
[2,]  1.933977  5.8501784 -1.70504980  0.7195951  1.4252209 -3.11543738
[3,]  1.290122 -1.7050498  3.31434984 -0.6324029  0.1860666 -0.08234236
[4,] -1.462717  0.7195951 -0.63240294  5.4179467  0.9003576 -3.61864495
[5,] -1.565595  1.4252209  0.18606662  0.9003576  4.5248002  0.52702347
[6,] -1.820834 -3.1154374 -0.08234236 -3.6186449  0.5270235  6.02038872
> eigen(mat)$values
[1] 11.4213448  7.3302845  5.7033748  3.9863332  0.4827576  0.1241385

Here my goal is to find the "nearest matrix" of "mat" for which the minimum
eigen value is 0.20 (I would rather want to fix some arbitrary value). While
finding that nearest matrix, I would like to keep all other properties
(whatever are those) of my original matrix "mat" as unaltered as possible.

Is there any algorithm to achieve that?

Thanks for your help.

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