日時： ２０１４年１月９日（木） １８：００～
場所： 東京大学　本郷キャンパス　工学部１４号館５階５３４号室
講演者：Brian Sutton （Department of Mathematics, Randolph-Macon College, USA）
タイトル：A Numerical Look at Quotients of the Orthogonal Group
概要： The problem of measuring distance between a pair of linear subspaces was considered several times between 1875 and 1975 by researchers including Jordan, Hotelling, Davis, Kahan, James, Wilkinson, Bj\"{o}rck, and Golub. Just missing the one-hundredth anniversary of Jordan's pioneering work, in 1977 Stewart formulated the CS decomposition, translating the geometric problem of measuring angles into an algebraic problem of computing a matrix decomposition. We will review this material and then extend the discussion to flags, i.e., nested sequences of linear subspaces. We will argue that the geometric problem of finding geodesics on the flag manifold can be reduced to an algebraic problem of computing canonical representatives in the quotient group O(n)/(O(k_1)\cdots O(k_p)). An algorithm for computing the canonical representatives will be presented.

詳細： http://nla.na.cse.nagoya-u.ac.jp/