Timeline for Condition for 3×3 block matrix to be stable
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Apr 27, 2023 at 3:58 | comment | added | Iosif Pinelis | @Zishuo : The problem of characterizing all such $M$ seems much harder. You may want to post it separately. I will have it in mind anyway. | |
| Apr 27, 2023 at 3:46 | comment | added | Zishuo | Yeah. Sorry, I just noticed that my way of asking is finding "a" $M$. Then your answer fully solves my problem and I have accepted the answer. The problem in the background is to find all such $M$. If you have any ideas welcome to share. | |
| Apr 27, 2023 at 3:43 | vote | accept | Zishuo | ||
| Apr 27, 2023 at 3:36 | comment | added | Iosif Pinelis | @Zishuo : Your request was to "design a symmetric positive definite matrix $M\in\mathbb{R}^{n\times n}$ and positive scalar $\alpha$ such that" -- emphasis mine. Isn't this request completely fulfilled now? | |
| Apr 27, 2023 at 3:30 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Apr 27, 2023 at 3:30 | comment | added | Zishuo | This answer finds all such $M,\alpha$ when $M$ and $H$ can be mutually diagonalizable. But for the scenario where $M$ is not a diagonal matrix after $H$ has been diagonalized, there may be choices of $M$ such that $A$ is stable. Nevertheless, @iosif-pinelis solves 99% of my question. Thank you! | |
| Apr 27, 2023 at 3:27 | comment | added | Iosif Pinelis | @Zishuo : Thank you for your comment. This typo is now fixed. Do you have other concerns about this answer? | |
| Apr 27, 2023 at 3:25 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Apr 27, 2023 at 3:21 | comment | added | Zishuo | This is really a nice answer. But this sentence may contain a typo: "So, $\lambda$ is a nonzero eigenvalue of $A$ iff $d(\lambda)=1$" should be "$d(\lambda)=0$". . | |
| Apr 26, 2023 at 21:35 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Apr 26, 2023 at 21:17 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Apr 26, 2023 at 21:12 | comment | added | Iosif Pinelis | The answer is now completed "by hand". | |
| Apr 26, 2023 at 21:09 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Apr 26, 2023 at 19:21 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |