When solving a system of linear first order differential equations, if the eigenvalues are repeated, we need a slightly different form of our solution to ensure linear indepence.
You know I have spent on this topic maybe 3 whole days with none sense info either online or from my tutor in the uni neither from these bad explanations books that he has recommended I have spent all day today searching online until I found you , many thanks for your effort and marvellous teaching you are amazing tutor please keep up I understand now how to work it out you make my day I have exam after 3 days many thanks
Could you do an example where the system gives repeated eigenvalues and the one value produces 2 linearly independent eigenvectors? I believe this kind of system will have a proper node also called star point.
You'll only have the intuition if you have enough background knowledge of the subject. At the level of math for this video, its already understood that we can find eigenvalues which relate to matrices and the intuition comes from choosing the form of the solution and plugging it into the original system of differential equations. Then we find out about eigenvectors. This is how we find solutions. Then once we get repeating eigenvalues we need to gain new intuition. In this video he finds the one eigenvector and then has to do a new technique to find a second eigenvector called a generalized eigenvector to find a second solution.
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You sound like a distant relative of Squidward. I don’t know why this occurred to me while I was listening. I don’t mean any offense.
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You know I have spent on this topic maybe 3 whole days with none sense info either online or from my tutor in the uni neither from these bad explanations books that he has recommended I have spent all day today searching online until I found you , many thanks for your effort and marvellous teaching you are amazing tutor please keep up I understand now how to work it out you make my day I have exam after 3 days many thanks
Thanks for making this video. Wonderful explanation.
Thank you so much. Straight to the point!
the most clearest vid on this topic out there
Most clear video I have come across. Thank!
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Thanks for such useful video
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Could you do an example where the system gives repeated eigenvalues and the one value produces 2 linearly independent eigenvectors? I believe this kind of system will have a proper node also called star point.
Very well explained!
Clear expression, thank you.
thank you so much!! explained it perfectly
Thank you, really easy to follow!
Thnks
thanks for the help!
Danki
perfect
superb
Thanks
Solving systems of differential equations by the method of eigenvectors and eigenvalues
yes, that is the topic lol
Why do people teach like this ? There is no intuition here. No understanding. What's the point.
It can work as a review if you kinda understand the concept and this kind of thing is kinda repeated throughout the course. That’s what I think
You'll only have the intuition if you have enough background knowledge of the subject. At the level of math for this video, its already understood that we can find eigenvalues which relate to matrices and the intuition comes from choosing the form of the solution and plugging it into the original system of differential equations. Then we find out about eigenvectors. This is how we find solutions. Then once we get repeating eigenvalues we need to gain new intuition. In this video he finds the one eigenvector and then has to do a new technique to find a second eigenvector called a generalized eigenvector to find a second solution.