Timeline for For what values of $k$ is matrix $k A - B$ positive semidefinite?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 30, 2010 at 17:36 | vote | accept | daizhuo | ||
| Nov 30, 2010 at 17:35 | comment | added | daizhuo | Thanks. In fact, $B_{13}$ must be 0. Let $P_1$ be a matrix consisting of columns that form a basis of the range of $A$. Let $P_2$ be a matrix consisting of columns that form a basis of the intersection of the kernel of $A$ and the range of $B$. Let $P_3$ be a matrix consisting of columns that form a basis of the intersection of the kernel of $A$ and the kernel of $B$. Then columns of $P=(P_1, P_2, P_3)$ form a basis of $\mathbb{R}^n$ in which $A$ and $B$ took the form you showed above. In particular, $B_{13} = P_1^T B P_3 = 0$ because $B P_3 = 0$. | |
| Nov 30, 2010 at 7:58 | history | edited | Denis Serre | CC BY-SA 2.5 |
added 24 characters in body
|
| Nov 30, 2010 at 1:00 | history | answered | Denis Serre | CC BY-SA 2.5 |