Minimal Matrices and the corresponding Minimal Curves on Flag manifolds in low dimension

E. ANDRUCHOW; L. E. MATA-LORENZO; A. MENDOZA; L. RECHT; ALEJANDRO VARELA

LINEAR ALGEBRA AND ITS APPLICATIONS

ELSEVIER SCIENCE INC

Año: 2009 vol. 430 p. 1906 - 1928

0024-3795

In general C∗-algebras, elements with minimal norm in some equivalence class are introduced and characterize We study the set of minimal hermitian matrices, in the case where the C∗-algebra consists of 3×3 complex matric and the quotient is taken by the subalgebra of diagonal matrices. We thoroughly study the set of minimal matric particularly because of its relation to the geometric problem of finding minimal curves in flag manifolds. For t flag manifold of ‘four mutually orthogonal complex lines’ in C4, it is shown that there are infinitely many minim curves joining arbitrarily close points. In the case of the flag manifold of ‘three mutually orthogonal compl lines’ in C3, we show that the phenomenon of multiple minimal curves joining arbitrarily close points does n occur. Key words: aproximation, curves, flag manifolds, matrices, minimal.∗-algebras, elements with minimal norm in some equivalence class are introduced and characterize We study the set of minimal hermitian matrices, in the case where the C∗-algebra consists of 3×3 complex matric and the quotient is taken by the subalgebra of diagonal matrices. We thoroughly study the set of minimal matric particularly because of its relation to the geometric problem of finding minimal curves in flag manifolds. For t flag manifold of ‘four mutually orthogonal complex lines’ in C4, it is shown that there are infinitely many minim curves joining arbitrarily close points. In the case of the flag manifold of ‘three mutually orthogonal compl lines’ in C3, we show that the phenomenon of multiple minimal curves joining arbitrarily close points does n occur. Key words: aproximation, curves, flag manifolds, matrices, minimal.∗-algebra consists of 3×3 complex matric and the quotient is taken by the subalgebra of diagonal matrices. We thoroughly study the set of minimal matric particularly because of its relation to the geometric problem of finding minimal curves in flag manifolds. For t flag manifold of ‘four mutually orthogonal complex lines’ in C4, it is shown that there are infinitely many minim curves joining arbitrarily close points. In the case of the flag manifold of ‘three mutually orthogonal compl lines’ in C3, we show that the phenomenon of multiple minimal curves joining arbitrarily close points does n occur. Key words: aproximation, curves, flag manifolds, matrices, minimal.C4, it is shown that there are infinitely many minim curves joining arbitrarily close points. In the case of the flag manifold of ‘three mutually orthogonal compl lines’ in C3, we show that the phenomenon of multiple minimal curves joining arbitrarily close points does n occur. Key words: aproximation, curves, flag manifolds, matrices, minimal.C3, we show that the phenomenon of multiple minimal curves joining arbitrarily close points does n occur. Key words: aproximation, curves, flag manifolds, matrices, minimal.Key words: aproximation, curves, flag manifolds, matrices, minimal.