Definitions of a subspace
Aviation-Definitions of a subspace
Resource Sample
Algebra Definitions
Subspace: A subspace is a defined space within a vector space, such as R2, R3 etc. The set of vectors, W, is a subspace of the vector space, V, iff: 1. The zero vector, 0, is a member of W 2. If the vectors, u and v are members of W, then u+v is a member of W also 3. If the vector u is a member of W and t is a Real Number then t*u is a member of W ***Note that statement 2 and statement 3 represent closure under addition and multiplication, respectively*** Basis: A basis is the minimal set of linearly independent vectors that span (generate) a subspace (ie. They are the minimal ingredients required to formulate any vector in the subspace). A set of vectors, B, is a basis for the subspace, V, iff the vectors in B are linearly independent and span (generate) V. Because the set B spans the subspace V, any vector in V can be written as a linear combination of the vectors ...
Resource Topics
Relevant Resources
