Thanks David for your pointer. Here my original matrix is VCV matrix which
is the utmost important matrix in finance. However in reality what happens
is that due to incomplete data. lot of missing values (or some other
problems) that matrix may be unstable like min eigen value is negative or
very close to zero etc.

My goal is to make that unstable matrix stable for further calculation. Here
I want to make the min eigen "quite far from zero in positive quadrant",
however still do not want to loose much information that is hidden in my
original matrix (what I call it "Real information").

I want to have a control on: How far min eigen value I want from zero.

Please let me should I need to give more information.

Thanks,
On Thu, Jul 21, 2011 at 9:27 AM, David Winsemius <dwinsemius@comcast.net>wrote:

>
> On Jul 20, 2011, at 11:17 PM, B. Jonathan B. Jonathan wrote:
>
>  It is not any homework problem. I just need some pointer. Given that I
>> think
>> I would be able to carry forward.
>>
>
> Then what kind of problem _is_ it? You say:
>
> "nearest matrix"   ... using what measure for distance or similarity?
>
> "... keep all other properties (whatever are those) of my original matrix
> "mat" as unaltered as possible."
>
>     ... this really does leave your question looking ... what would be
> kind? ... perhaps the word "nebulous" would be apt? How are we supposed to
> make choices for you in the absence of any goals?
>
> --
> David
>
>
>
>> Thanks,
>>
>> On Thu, Jul 21, 2011 at 4:52 AM, Bert Gunter <gunter.berton@gene.com>
>> wrote:
>>
>>  A homework problem?
>>> -- Bert
>>>
>>> On Wed, Jul 20, 2011 at 10:06 AM, B. Jonathan B. Jonathan
>>> <bkheijonathan@gmail.com> wrote:
>>>
>>>> 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.
>>>>
>>>
>
>
> David Winsemius, MD
> West Hartford, CT
>
>

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