Timeline for Invertibility of a certain matrix indexed by the Hamming cube
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 9, 2013 at 1:31 | comment | added | Sungjin Kim | With help of Benjamin Young's and Brendan McKay's answers, I found that Brendan's guess is true without $n$ on the exponent. Then tried understanding the combinatorial meaning behind it. The formula $AM=I$ is essentially $(1-1)^m=0$ for $m>0$. | |
| Mar 8, 2013 at 10:07 | vote | accept | Yemon Choi | ||
| Mar 8, 2013 at 10:07 | |||||
| Mar 8, 2013 at 8:33 | history | edited | Sungjin Kim | CC BY-SA 3.0 |
Added a comment about inverse.
|
| Mar 8, 2013 at 1:58 | comment | added | Yemon Choi | Apologies for vagueness, your comment is a fair one. I have updated the question with an attempt to clarify. | |
| Mar 8, 2013 at 0:54 | comment | added | Benjamin Steinberg | I gave this a +1. It is no less conceptual than computing the inverse by induction and in a sense it is very much like the first answer except without determinants. I liked all the answers. | |
| Mar 7, 2013 at 19:48 | comment | added | Sungjin Kim | The word "conceptual" is really vague in your original posting. What I understand is that my solution is involving the "concept" of "elementary row and column operations don't change the rank of matrix". Here is what I see: Kevin's answer is involving "invertible <=> nonzero determinant" Benjamin Steinberg's answer is involving "change of basis" Benjamin Young's answer is involving "the very definition of invertibility". So, I don't see why mine is specifically what you don't want to see. | |
| Mar 7, 2013 at 19:00 | comment | added | Yemon Choi | I explicitly said I wanted a more "conceptual" argument. Of course induction is involved somewhere, but what I wanted was some explanation of how this example might fit into a bigger picture | |
| Mar 7, 2013 at 10:07 | history | edited | Sungjin Kim | CC BY-SA 3.0 |
added 12 characters in body
|
| Mar 7, 2013 at 9:53 | history | answered | Sungjin Kim | CC BY-SA 3.0 |