linear algebra - if $T: V\to V$ and $ dim (KerT)+dim (ImT)=dimV
Mar 29, 2023 · $KerT+ImT=dimV$ ? Is this possible? $Ker T, Im T$ are subspaces of $V$ and $dimV$ is a just a...
Prove that $T^*$ is injective iff $ImT$ Is dense
Dec 21, 2014 · Let X,Y be two normed spaces, and $T:X\rightarrow Y$ a bounded linear operator. prove that the adjoint operator $T^*$ ($T^*f (x)=f (Tx)$ is injective iff $ImT$ is dense
V = ImT \\oplus \\ KerT - Mathematics Stack Exchange
Linear Tranformation that preserves Direct sum V = ImT ⊕ KerT Ask Question Asked 12 years, 10 months ago Modified 12 years, 10 months ago
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, 5 months ago Modified 6 years, 5 months ago
linear algebra - Prove Ker$T= ($Im$T^*)^\bot$ and …
May 26, 2023 · Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges,
Intersection of the NullT and ImT - Mathematics Stack Exchange
Feb 11, 2015 · Intersection of the NullT and ImT Ask Question Asked 10 years, 7 months ago Modified 4 years, 7 months ago
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 ...
Give an example of a linear map $T$ such that $\dim …
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 …
Example of linear transformation on infinite dimensional vector …
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 …
If $Ker (T^2)=Ker (T)$ show that $V=Ker (T)\oplus Im (T)$
Nov 8, 2015 · You don't have enough information to conclude $T = T^2$. Consider rotating the plane through $\pi/2$ radians...