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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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