abstract vector spaceの例文
- In mathematical language, all possible pure states of a system form an abstract vector space called Hilbert space, which is typically infinite-dimensional.
- The definition of a " vector " in physics ( including both polar vectors and pseudovectors ) is more specific than the mathematical definition of " vector " ( namely, any element of an abstract vector space ).
- For example, the set of all possible 4d orbitals ( i . e ., the five states " m " =-2,-1, 0, 1, 2 and their quantum superpositions ) form a 5-dimensional abstract vector space.
- Further, all these spaces are intrinsically defined they do not require a choice of basis in which case one rewrites this in terms of abstract vector spaces, operators, and the dual spaces as A \ colon V \ to W and A ^ * \ colon W ^ * \ to V ^ * : the kernel and image of A ^ * are the cokernel and coimage of A.
- For an abstract vector space " V " ( rather than the concrete vector space K ^ n ), or more generally a center of the endomorphism algebra, and similarly invertible transforms are the center of the general linear group GL ( " V " ), where they are denoted by Z ( " V " ), follow the usual notation for the center.
