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 …
linear algebra - if $T: V\to V$ and $ dim (KerT)+dim (ImT)=dimV $ can i ...
Mar 29, 2023 · Why do you include the rank-nullity theorem ("$ dim (KerT)+dim (ImT)=dimV $") as an hypothesis in your title?
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 Base for ImT and KerT - Mathematics Stack Exchange
Linear Alegbra - Find Base for ImT and KerT Ask Question Asked 11 years, 6 months ago Modified 11 years, 6 months ago
V = ImT \oplus \ KerT - Mathematics Stack Exchange
Linear Tranformation that preserves Direct sum $ V = ImT \oplus \ KerT $ Ask Question Asked 13 years, 2 months ago Modified 13 years, 2 months ago
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?
Whether the image is a subspace of a linear transformation
Aug 9, 2016 · Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant …
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 …
Find the weak sequential closure of a set in $L^2 (-\pi,\pi)$
$A=\ {f_ {m,n} (t)|0\le m<n\}$ where $f_ {m,n} (t)=e^ {imt}+me^ {int}$. I should find the weak sequential closure of $A\subset L^2 (-\pi,\pi)$. I know what I'm ...
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 …