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Positive Semi definite matrix and Cholesky
Posted: July 18th, 2005, 8:05 pm
by khamsing
Hi everyone!I am probably going to ask a silly question but I used the Cholesky VBA code found in Wilmott on Quanitative finance and so far all the correlation matrix I have could be factorize. Does than mean that all my matrix are positive semi definite? Many thanks in advance!
Positive Semi definite matrix and Cholesky
Posted: July 19th, 2005, 1:16 pm
by Antonio
You're dealing with correlation matrix, therefore...
Positive Semi definite matrix and Cholesky
Posted: July 19th, 2005, 2:12 pm
by Tomski
Use the methods proposed by Peter Jackel (spectral sqaure root of symmetric matrix) rather than cholesky.
Positive Semi definite matrix and Cholesky
Posted: July 20th, 2005, 3:18 am
by AlphaNumericus
Suppose, for example, your matrix has the historical covariances of various spot fx rates (to USD). Suppose one of the currencies is tied to a basket of other currencies, i.e. its exchange rate is always the same linear combination of some other currencies' exchange rates to USD. Then it will give rise to a zero eigenvalue and Choleski will fail. Choleski needs positive definite matrices to work, while correlation matrices may be non-negative definite.