Oliver Sourbut comments on Linear Algebra Done Right, Axler

Oliver Sourbut 5 Jan 2023 11:17 UTC
7 points
0
This is great! I’ll thread a few nits under this comment
- Oliver Sourbut 5 Jan 2023 11:22 UTC
  9 points
  2
  Parent
  
  We call a subspace $S \subset V$ invariant under $f \in L (V)$ if, for all $\to s \in S$ ,
  
  $f (\to s) = \to s$
  
  should read
  
  $f (\to s) \in S$
- Oliver Sourbut 5 Jan 2023 11:19 UTC
  8 points
  2
  Parent
  
  Let $S$ now specifically be a one-dimensional subspace of $V$ such that, for all $\to v \in V$ ,
  
  $S = {a \to v : a \in F}$
  
  I think such $S$ can not exist in most cases, and it should instead read ‘… for some $\to v \in V$ …’
  
  The expression for $S$ is describing the span of the vector $\to v$ , so certainly if $V$ is more than one-dimensional, if some subspace $S$ has this property for all $\to v \in V$ then it has this property for linearly independent vectors in $V$ , which is a contradiction.