Question

I want to show that Nullspace (normed space) is a vector space. can someone help

Answer 1

null spaces are defined reference to some linear transformation

Answer 2

yes. I mean a linear transformation on a normed vector space

Answer 3

so u want to show it a subspace?

Answer 4

yes

Answer 5

the condition is, for x,y in space n a, b scalars
ax+by must belong to the space...right?

Answer 6

i think so, if that is enough to show

Answer 7

\[x, y \in N\]

Answer 8

then \[T ( x )= T ( y ) = 0\]

Answer 9

T (ax + by) = a T(x) +bT(y)
using the linarity

Answer 10

T (ax + by) = a T(x) +bT(y)=0
showing that ax + by is in N

Answer 11

so N is the vector subspace