In functional analysis, a branch of mathematics, a unitary operator is a bounded linear operator U : H → H on a Hilbert space H satisfying where U is the adjoint of U, and I : H → H is the identity operator. This property is equivalent to the following: The range of U is dense, and U preserves the inner product 〈, 〉 on the Hilbert space, i.e. for all vectors x and y in the Hilbert space, To see this, notice that U preserves the inner product implies U is an isometry.
Hula is a small village in southern Lebanon on the southern side of the Litani river near the Lebanese-Israeli borders. It is located 750 meters above the sea-level. It is populated by 100% shiite Muslims and the villagers have a very bad relationship with Israel. In some areas the village is called "The Door Of Freedom" do to its fraught history of being the first village to be occupied by Israel and was the first village to retaliate and win it's freedom followed by the country as a whole.
The Bibliotheca Palatina of Heidelberg was the most important library of the German Renaissance, numbering approximately 5,000 printed books and 3,524 manuscripts. In the 1430s, Elector Louis III founded the Stiftsbibliothek in the Heiliggeistkirche, which had good light for reading. This library formed the core of the Palatine Collection established by Elector Ottheinrich in the 1550s, together with the University Library Heidelberg.