- #1
bigheadsam
- 4
- 0
Hi all,
I have some questions about the concept of subspace of linear transformation and its dimension, when I try to prove following problems:
Prove T is a finite dimensional subspace of L(V) and U is a finite dimensional subspace of V, then
T(U) = {F(u) | F is in T, u is in U} is a subspace of V,
Dim(T(U))<=(dim(T))(dim(U))
What does “T is a finite dimensional subspace of L(V)” mean?
L1(v)+L2(v) = (L1+L2)(v)
aL1(v) = (aL1)(v) ?
and what is dim(T) and dim(T(U))?
Every Linear transformation has its Matrix format, dim(T) is dim(M(T))?
I am a fish in Linear algebra. Hope I explain my questions clearly.
I have some questions about the concept of subspace of linear transformation and its dimension, when I try to prove following problems:
Prove T is a finite dimensional subspace of L(V) and U is a finite dimensional subspace of V, then
T(U) = {F(u) | F is in T, u is in U} is a subspace of V,
Dim(T(U))<=(dim(T))(dim(U))
What does “T is a finite dimensional subspace of L(V)” mean?
L1(v)+L2(v) = (L1+L2)(v)
aL1(v) = (aL1)(v) ?
and what is dim(T) and dim(T(U))?
Every Linear transformation has its Matrix format, dim(T) is dim(M(T))?
I am a fish in Linear algebra. Hope I explain my questions clearly.