Namespaces
Variants
Actions

Unitary space

From Encyclopedia of Mathematics
Revision as of 17:23, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

A vector space over the field of complex numbers, on which there is given an inner product of vectors (where the product of two vectors and is, in general, a complex number) that satisfies the following axioms:

1) ;

2) ;

3) ;

4) if , then , i.e. the scalar square of a non-zero vector is a positive real number.

A unitary space need not be finite-dimensional. In a unitary space one can, just as in Euclidean spaces, introduce the concept of orthogonality and of an orthonormal system of vectors, and in the finite-dimensional case one can prove the existence of an orthonormal basis.


Comments

References

[a1] W. Noll, "Finite dimensional spaces" , M. Nijhoff (1987) pp. 338
[a2] W.H. Greub, "Linear algebra" , Springer (1975) pp. Chapt. XI
How to Cite This Entry:
Unitary space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Unitary_space&oldid=17853
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article