High Quality Content by WIKIPEDIA articles! Systems of unisolvent functions are much more common in 1 dimension than in higher dimensions. In dimension d = 2 and higher (? ? Rd), the functions 1, 2, ..., n cannot be unisolvent on ? if there exists a single open set on which they are all continuous. To see this, consider moving points x1 and x2 along continuous paths in the open set until they have switched positions, such that x1 and x2 never intersect each other or any of the other xi. The determinant of the resulting system (with x1 and x2 swapped) is the negative of the determinant of the initial system. Since the functions i are continuous, the intermediate value theorem implies that some intermediate configuration has determinant zero, hence the functions cannot be unisolvent.

Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.