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NotEuler's latest activity
N
NotEuler
replied to the thread
I
Is there always a matrix corresponding to eigenvectors?
.
Thanks Hill and fresh_42. Perhaps I was again confusing vectors with their coordinates, like you mentioned very early on. I'll try to...
Feb 3, 2024
N
NotEuler
reacted to
fresh_42's post
in the thread
I
Is there always a matrix corresponding to eigenvectors?
with
Like
.
No. This depends on the transformation matrix and its properties (being diagonal, orthogonal, etc.). A vector ##\vec{x}## and a linear...
Feb 3, 2024
N
NotEuler
reacted to
Hill's post
in the thread
I
Is there always a matrix corresponding to eigenvectors?
with
Like
.
No, it is not, but you don't need it. You got a matrix for which one of your vectors is a left eigenvector and another is a right...
Feb 3, 2024
N
NotEuler
replied to the thread
I
Is there always a matrix corresponding to eigenvectors?
.
Ok, I am making progress. But now I am stuck with one thing: so the diagonal matrix in post 2 is symmetric. But once it is transformed...
Feb 2, 2024
N
NotEuler
replied to the thread
I
Is there always a matrix corresponding to eigenvectors?
.
Ok, I found my mistake and managed to replicate what you describe here. That diagram is really really helpful for my understanding of...
Feb 2, 2024
N
NotEuler
replied to the thread
I
Is there always a matrix corresponding to eigenvectors?
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Many thanks for your time and effort! I am really learning a lot from this. I thought that is what I did earlier in my 'experiments'...
Feb 1, 2024
N
NotEuler
replied to the thread
I
Is there always a matrix corresponding to eigenvectors?
.
I tried to do this but I don't think I understand it yet. So should the basis transformation matrix be formed of the eigenvectors a1 and...
Feb 1, 2024
N
NotEuler
replied to the thread
I
Is there always a matrix corresponding to eigenvectors?
.
True. I didn't really think of that. And in that case, I should rephrase my question as 'Can I be sure a _non-zero_ matrix exists that...
Feb 1, 2024
N
NotEuler
replied to the thread
I
Is there always a matrix corresponding to eigenvectors?
.
Thanks very much for all this. I shall think on it and hopefully I'll eventually get my head around it!
Jan 31, 2024
N
NotEuler
replied to the thread
I
Is there always a matrix corresponding to eigenvectors?
.
Yes, I think I partially get this. I should not be thinking of the vectors as entities tied to one specific coordinate system, but more...
Jan 31, 2024
N
NotEuler
replied to the thread
I
Is there always a matrix corresponding to eigenvectors?
.
Ok, thanks to both of you. I think I'll have to sit down with pen&paper and maybe a book or two to figure this out...!
Jan 31, 2024
N
NotEuler
replied to the thread
I
Is there always a matrix corresponding to eigenvectors?
.
Thanks! But I'm not sure if this is the same question? You are talking about two eigenvectors to two different eigenvalues. My...
Jan 31, 2024
N
NotEuler
posted the thread
I
Is there always a matrix corresponding to eigenvectors?
in
Linear and Abstract Algebra
.
I tried to find the answer to this but so far no luck. I have been thinking of the following: I generate two random vectors of the same...
Jan 31, 2024
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