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File: Matrix Pdf 173039 | Fun11 Finance
functions of matrices and researchmatters nearest correlation matrices february 25 2009 nick higham nick higham school of mathematics director of research theuniversity of manchester school of mathematics higham ma man ...

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                  Functions of Matrices and
                   ResearchMatters
                Nearest Correlation Matrices
                     February 25, 2009
                            Nick Higham
                        Nick Higham
                      School of Mathematics
                    Director of Research
                   TheUniversity of Manchester
                   School of Mathematics
                      higham@ma.man.ac.uk
             http://www.ma.man.ac.uk/~higham/
                                                           1 / 6
                                                                                                                                                                                                                                                                                                                                                                                                                                   It is
                                                                                                                                                                                                                                                                                                                                                                                                                                         −1
                                                                                                                                                                                                                                                                                                                                                                                                                                       A ,
                                                                                                                                                                                                                                                                                                                                                                                                                                       eA,
                                                                                                                                                                                                                                                                                                                                                                                                                                       √
                                                                                                                                                                                                                                                                                                                                                                                                                                         A,
                                                                                                                                                                                                                                                                                                                                                                                                                                       . . .
   Whatis a Matrix Function?
     It’s not
          det(A) or trace(A),
          elementwise evaluation: f(aij),
            T
          A ,
          matrix factor (e.g., A = LU).
  MIMS              Nick Higham                 Matrix Functions      2/ 33
   Whatis a Matrix Function?
     It’s not
          det(A) or trace(A),
          elementwise evaluation: f(aij),
            T
          A ,
          matrix factor (e.g., A = LU).
     It is
            −1
          A ,
          eA,
          √
            A,
          . . .
  MIMS              Nick Higham                 Matrix Functions      2/ 33
   Cayley and Sylvester
          Term “matrix” coined in 1850
          by James Joseph Sylvester,
          FRS(1814–1897).
          Matrix algebra developed by
          Arthur  Cayley,   FRS (1821–
          1895).
          Memoir on the Theory of Ma-
          trices (1858).
  MIMS            Nick Higham                Matrix Functions     3/ 33
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...Functions of matrices and researchmatters nearest correlation february nick higham school mathematics director research theuniversity manchester ma man ac uk http www it is a ea whatis matrix function s not det or trace elementwise evaluation f aij t factor e g lu mims cayley sylvester term coined in by james joseph frs algebra developed arthur memoir on the theory trices...

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