Relation To Bases
If the set is a frame of V, it spans V. Otherwise there would exist at least one non-zero which would be orthogonal to all . If we insert into the frame condition, we obtain
therefore, which is a violation of the initial assumptions on the lower frame bound.
If a set of vectors spans V, this is not a sufficient condition for calling the set a frame. As an example, consider and the infinite set given by
This set spans V but since we cannot choose . Consequently, the set is not a frame.
Read more about this topic: Frame Of A Vector Space
Famous quotes containing the words relation to, relation and/or bases:
“Among the most valuable but least appreciated experiences parenthood can provide are the opportunities it offers for exploring, reliving, and resolving one’s own childhood problems in the context of one’s relation to one’s child.”
—Bruno Bettelheim (20th century)
“Among the most valuable but least appreciated experiences parenthood can provide are the opportunities it offers for exploring, reliving, and resolving one’s own childhood problems in the context of one’s relation to one’s child.”
—Bruno Bettelheim (20th century)
“In the beginning was the word, the word
That from the solid bases of the light
Abstracted all the letters of the void....”
—Dylan Thomas (1914–1953)