UM ETheses Collection (澳門大學電子學位論文庫)
 Title

Distance to the convex hull of an equivalence class by special orthogonal equivalence
 English Abstract

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In this thesis, we study an approximation problem in the n x n real matrix space Mₙ (R). Two matrices A,B ∈ Mₙ(R) are said to be special orthogonal equivalent if there exist n x n special orthogonal matrices U and V such that A= UBV. A norm ║║ on Mₙ(R) is said to be special orthogonally invariant if ║UAV║=║A║for any n x n special orthogonal matrices U, V. Let B/~ be the equivalence class of B by special orthogonal equivalence and let conv B/~ denote its convex hull, i.e., the smallest convex set containing B/~. Given A, B ∈ Mₙ(R) and a special orthogonally invariant norm║║, we determine the quantities max{║A  X║: X ∈ conv B/~ } and min{║A  X║: X ∈ conv B/~ }. It turns out that we can find matrices B and Bₘ in conv B/~ such that ║A  Bₘ║ ≤ ║A  X║ ≤ ║A  B║ for all X ∈ conv B/~, and the pair of matrices work for all special orthogonally invariant norms. The problem is ultimately amount to solving an approximation problem in Rⁿ, which is of independent interests.
 Issue date

2000.
 Author

Sou, Man Chong
 Faculty

Faculty of Science and Technology
 Department

Department of Mathematics
 Degree

M.Sc.
 Subject

Matrix inequalities
Orthogonalization methods
 Supervisor

Cheng, Che Man
 Files In This Item
 Location
 1/F Zone C
 Library URL
 991008431959706306