Timeline for Singular values of the sum of A and A^T
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Jan 4, 2013 at 22:30 | comment | added | Daniel86 | @alex o. - If $P$ is diagonally dominant but not necessarily symmetric, $P+P^{T}$ is diagonally dominant and symmetric and hence positive definite. However, for $A=P^{k}$ this is not always the case. For such a case, I want to lower bound the smallest singular value of $A+A^{T}$ in terms of the singular values of $P$. | |
| Jan 4, 2013 at 21:24 | comment | added | alex o. | @Daniel86 - under standard definitions, a real positive definite matrix is automatically symmetric. When you use the words "positive definite" I am guessing you mean that $x^T A x > 0$ for any $x \in R^n$ but $A$ is not necessarily symmetric. Is my understanding correct? | |
| Jan 3, 2013 at 6:31 | comment | added | Daniel86 | Thankyou, it is a nice example, but can this situation occur where $A$ is an integer power of a positive definite matrix? I edited my original post. Thanks. | |
| Jan 2, 2013 at 22:43 | history | answered | alex o. | CC BY-SA 3.0 |