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JJH
JJH
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Let $P_n$ be the space of polynomials in $n$ variables over a field of characteristic 0. I'm very sure that the space spanned by powers of linear functions is the whole space $P_n$. Anyone can come up with a proof, or indicate a proofreference for it? Thanks a lot.

Let $P_n$ be the space of polynomials in $n$ variables. I'm very sure that the space spanned by powers of linear functions is the whole space $P_n$. Anyone can come up with a proof, or indicate a proof for it? Thanks a lot.

Let $P_n$ be the space of polynomials in $n$ variables over a field of characteristic 0. I'm very sure that the space spanned by powers of linear functions is the whole space $P_n$. Anyone can come up with a proof, or indicate a reference for it? Thanks a lot.

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JJH
JJH
  • 1.5k
  • 8
  • 19

Powers of linear functions span the space of polynomial functions?

Let $P_n$ be the space of polynomials in $n$ variables. I'm very sure that the space spanned by powers of linear functions is the whole space $P_n$. Anyone can come up with a proof, or indicate a proof for it? Thanks a lot.