Part 16 : Dimension and Basis
Published in
Mar 20, 2019
For a set of vectors, say V.
V = {v1, v2, v3, …………………., vn}
The maximum number of linearly independent vectors in V will be called dimension of V. Represented as dim(V).
So, if v1 and v2 are the only linearly independent vectors in V. Then dim(V)=2
Basis
The largest set of linearly independent vectors in set V is called Basis of set V.
Basis(V) = {v1, v2}
If we add one or more vectors from set V into Basis, the set will become linearly dependent.
The number of elements in basis is equal to dimension.
Dimensions of Four Fundamental Subspaces
For a matrix A,
of order = m×n
and rank = r,
the dimensions of four fundamental subspaces will be
