Should be "scalar or vector". I'm interested in the loss of precision
by dimensional reduction algorithms: matrix difference is only defined
for samesize matrices. So, there is no real absolute measure, just
relative measures that are not very useful except for certain use
cases.
On Sun, Dec 12, 2010 at 7:21 PM, Ted Dunning <ted.dunning@gmail.com> wrote:
> What do you mean by rank of a matrix? The normal definition is the number
> of nonzero singular values. This
> doesn't sound like what you mean.
>
> What do you mean by loss of information? If you mean how do you compare an
> approximation of a matrix
> versus the original, yes there are ways of doing that, not all very useful.
> Norm of the difference is one example
> that leads to least squares formulations.
>
> Also, is there something missing from the sentence with "scalar of vector"
> in it?
>
> On Sun, Dec 12, 2010 at 6:04 PM, Lance Norskog <goksron@gmail.com> wrote:
>
>> Given a matrix reduction algorithm, how do you measure the loss of
>> information perpetrated by the algorithm on the poor defenseless input
>> matrix?
>> Are there algorithms to compare two matrices and get a relative rank value?
>>
>> Is there a scalar of vector that describes the rank of a matrix? Then
>> you could just compare the two rank values.
>>
>> Is there a probabilistic approach to the problem?
>>
>> 
>> Lance Norskog
>> goksron@gmail.com
>>
>

Lance Norskog
goksron@gmail.com
