Timeline for Eigenspace of convex combination of two idempotent matrices
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Mar 11, 2016 at 9:47 | comment | added | Ilya Bogdanov | We know that $U_2\perp U$, and $H_1$ is the orthogonal projection onto $W_1$ which contains $U$. Thus yields that $H_1(U_2)\perp U$ as well. Moreover, $H_1(U_2)\subseteq W_1$; thus $H_1(U_2)$ lies in the orthogonal complement of $U$ in $W_1$, i.e., in $U_1$. | |
| Mar 11, 2016 at 9:21 | comment | added | Tobias Windisch | Thank you for your answer. Could please provide more details why $H_i(U_{3-i})\subseteq U_i$ is true? This seems to be important for a generalization. | |
| Mar 10, 2016 at 11:59 | history | edited | Ilya Bogdanov | CC BY-SA 3.0 |
deleted 2 characters in body
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| Mar 10, 2016 at 9:05 | history | answered | Ilya Bogdanov | CC BY-SA 3.0 |