Houjun Liu

Axler 2.C

Key Sequence

New Definitions

Results and Their Proofs

Questions for Jana

  • Example 2.41: why is it that \(\dim U \neq 4\)? We only know that \(\dim \mathcal{P}_{3}(\mathbb{R}) = 4\), and \(\dim U \leq 4\). Is it because \(U\) (i.e. basis of \(U\) doesn’t span the polynomial) is strictly a subset of \(\mathcal{P}_{3}(\mathbb{R})\), so there must be some extension needed? because we know that \(U\) isn’t all of \(\mathcal{P}_{3}\).

Interesting Factoids