linear algebra - if $T: V\to V$ and $ dim (KerT)+dim (ImT)=dimV $ can i ...
Mar 29, 2023 · $KerT+ImT=dimV$ ? Is this possible? $Ker T, Im T$ are subspaces of $V$ and $dimV$ is a just a...
V = ImT \oplus \ KerT - Mathematics Stack Exchange
Linear Tranformation that preserves Direct sum $ V = ImT \oplus \ KerT $ Ask Question Asked 12 years, 11 months ago Modified 12 years, 10 months ago
SageMath: Orthogonal projection of $\mathbb {C}^3$ onto a subspace.
Dec 13, 2024 · Now, my problem arises when I evaluate P_imT with specific values of a,b,c (in this case, the standard basis of $\mathbb {C}^3$) in order to obtain the columns of the projection matrix …
Prove that $T^*$ is injective iff $ImT$ Is dense
Dec 21, 2014 · The title of your question does not really match the actual question (maybe the statement of the current question is used to prove the result in the title?). Is this intended?
linear algebra - Prove Ker$T= ($Im$T^*)^\bot$ and (Ker$T^*$)$^\bot ...
May 26, 2023 · This means we have $v \in (ImT^*)^\bot$ and therfore we have $KerT \subseteq (ImT^*)^\bot$. For the other side, consider $0 \neq v \in (ImT^*)^\bot$, (which exists from the same …
Finding the basis of ker (T) and im (T) - Mathematics Stack Exchange
Jul 19, 2021 · for part d, would elaborate by showing that the image of $T$ is equal to the span of $\ {1,x\}$. Since you already know that $1$ and $x$ are linearly independent ...
Find a basis for KerT and ImT (T is a linear transformation)
Jun 15, 2019 · Find a basis for KerT and ImT (T is a linear transformation) Ask Question Asked 6 years, 6 months ago Modified 6 years, 6 months ago
Is it true that if $T$ is a linear operator on a finite-dimensional ...
If you knew that $\ker T \cap \operatorname {im} T= \emptyset$, then you'd have a proof. But this isn't true, and you can easily find an example in small dimensional spaces.
Give an example of a linear map $T$ such that $\dim (\operatorname ...
Jan 1, 2020 · This is completely correct. This will give a linear map with the properties you're asked for. I think that it is a bit too general to actually be "an example". I think it would be better if you actually …
Example of linear transformation on infinite dimensional vector space
May 22, 2018 · I haven't had much experience with infinite dimensional vector spaces, and I was working on a problem that asks to prove that for a finite dimensional vector space $V$, and linear …