»ã±¨±êÌâ (Title)£ºMatrices with the rank-preserving transversality property (±£ÖȺá½ØÐԵľØÕó)

»ã±¨ÈË (Speaker)£º Zhongshan Li ½ÌÊÚ£¨×ôÖÎÑÇÖÝÁ¢´óѧ£©

»ã±¨¹¦·ò (Time)£º2024Äê10 ÔÂ29 (Öܶþ) 9:00

»ã±¨µØÖ· (Place)£ºÌÚѶ»áÒ飺869-930-523

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»ã±¨ÌáÒª£º Given an $m\times n$ real matrix $A$, the set of all real matrices with the same size and the same rank as $A$ forms a smooth manifold. The set of all real matrices whose entries have the same sign as the corresponding entry of the matrix $A$ forms another smooth manifold. When the tangent spaces of these two manifolds at $A$ sum to $\mathbb R^{m\times n}$, we say that $A$ has the rank-preserving transversality property (RPTP). In this talk, we explore the RPTP. In particular, we present some fundamental results on the RPTP, the sign patterns and zero-nonzero patterns that require or allow the RPTP, and some open problems.