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...
Find the weak sequential closure of a set in $L^2 (-\pi,\pi)$
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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 …
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 …
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 Base for ImT and KerT - Mathematics Stack Exchange
Linear Alegbra - Find Base for ImT and KerT Ask Question Asked 11 years, 3 months ago Modified 11 years, 3 months ago
A probability problem about gifts - Mathematics Stack Exchange
Apr 25, 2025 · $$ \frac {c_m} { (kn)^m} = \frac {1} {2\pi} \int_0^ {2\pi} \left (1 + \frac {k^2} {kn}e^ {it} + \dots \right)^n e^ {-imt}dz \\ \to_ {n\to \infty} \frac {1} {2\pi} \int_0^ {2\pi} \exp\left ( ke^ {it} \right) e^ { …
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?
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, 8 months ago Modified 6 years, 8 months ago