Prove that for a real matrix $A$, $\ker (A) = \ker (A^TA)$
Is it possible to solve this supposing that inner product spaces haven't been covered in the class yet?
$\ker (A^TA) = \ker (A)$ - Mathematics Stack Exchange
Sep 9, 2018 · I am sorry i really had no clue which title to choose. I thought about that matrix multiplication and since it does not change the result it is idempotent? Please suggest a better …
How to find $ker (A)$ - Mathematics Stack Exchange
So before I answer this we have to be clear with what objects we are working with here. Also, this is my first answer and I cant figure out how to actually insert any kind of equations, besides …
If Ker (A)=$\ {\vec {0}\}$ and Ker (B)=$\ {\vec {0}\}$ Ker (AB)=?
Thank you Arturo (and everyone else). I managed to work out this solution after completing the assigned readings actually, it makes sense and was pretty obvious. Could you please …
linear algebra - Prove that $\ker (AB) = \ker (A) + \ker (B ...
It is not right: take $A=B$, then $\ker (AB)=\ker (A^2) = V$, but $ker (A) + ker (B) = ker (A)$.
I have the following matrix B and I need to find matrix A so that …
I think that the correct path is to show that ImB ⊆ KerA which is when AB=0 and KerA⊆ImB at the same time implies KerA=ImB. But I don't know when that is true. I also need to prove that A …
Prove that $\operatorname {im}\left (A^ {\top}\right) = \ker (A ...
I need help with showing that $\ker\left (A\right)^ {\perp}\subseteq Im\left (A^ {T}\right)$, I couldn't figure it out.
Can $RanA=KerA^T$ for a real matrix $A$? And for complex $A$?
Jan 27, 2021 · It does address complex matrices in the comments as well. It is clear that this can happen over the complex numbers anyway.
How to prove strong duality by Slater's condition without the ...
Feb 11, 2021 · In Section 5.3.2 of Boyd, Vandenberghe: Convex Optimization, strong duality is proved under the assumption that ker(A^T)={0} for the linear map describing the equality …
Linear transformations proof - Mathematics Stack Exchange
Dec 20, 2019 · Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and …