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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    null spaces are defined reference to some linear transformation

  2. anonymous
    • 5 years ago
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    yes. I mean a linear transformation on a normed vector space

  3. anonymous
    • 5 years ago
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    so u want to show it a subspace?

  4. anonymous
    • 5 years ago
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    yes

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

  6. anonymous
    • 5 years ago
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    i think so, if that is enough to show

  7. anonymous
    • 5 years ago
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    \[x, y \in N\]

  8. anonymous
    • 5 years ago
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    then \[T ( x )= T ( y ) = 0\]

  9. anonymous
    • 5 years ago
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    T (ax + by) = a T(x) +bT(y) using the linarity

  10. anonymous
    • 5 years ago
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    T (ax + by) = a T(x) +bT(y)=0 showing that ax + by is in N

  11. anonymous
    • 5 years ago
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    so N is the vector subspace

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