Direct sum of modules - Wikipedia: "The subspace V × {0} of V ⊕ W is isomorphic to V and is often identified with V; similarly for {0} × W and W. (See internal direct sum below.) With this identification, every element of V ⊕ W can be written in one and only one way as the sum of an element of V and an element of W. The dimension of V ⊕ W is equal to the sum of the dimensions of V and W. One elementary use is the reconstruction of a finite vector space from any subspace W and its orthogonal complement:
{\displaystyle \mathbb {R} ^{n}=W\oplus W^{\perp }}
This construction readily generalises to any finite number of vector spaces."
'via Blog this'
No comments:
Post a Comment