Timeline for Inverse of a matrix with binomial entries
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Aug 2, 2017 at 15:09 | comment | added | valle | Yes, thank you. I accepted your answer. | |
| Aug 2, 2017 at 15:09 | vote | accept | valle | ||
| Aug 2, 2017 at 15:01 | comment | added | G Cab | @becko; is everyhing (enough) clear now? | |
| Jul 26, 2017 at 21:52 | history | edited | G Cab | CC BY-SA 3.0 |
edited typo
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| Jul 26, 2017 at 20:13 | comment | added | G Cab | @becko: I added some notes to better clarify the meaning of matrix $\bf E$, and to show that inversion of (1) just involves simple manipulations around the same set of basic matrices. | |
| Jul 26, 2017 at 20:08 | history | edited | G Cab | CC BY-SA 3.0 |
added notes on inversion
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| Jul 26, 2017 at 13:22 | comment | added | valle | Yes, but you still have to invert $\mathbf{B}_h$, $\mathbf{St}_{2h}$ and $\mathbf{I}_h + \overline{\mathbf{E}_h}$, which I'm not sure how to do. In your notation, what does $(\mathbf{I}_h + \overline{\mathbf{E}_h})^\mathbf{a}$ mean? | |
| Jul 26, 2017 at 13:09 | comment | added | G Cab | @becko: and clearly, id. (1) can be easily inverted to get the formula for $\bf{M^{-1}}$ | |
| Jul 26, 2017 at 13:06 | history | edited | G Cab | CC BY-SA 3.0 |
added tags to formulas
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| Jul 26, 2017 at 12:58 | comment | added | G Cab | @becko: yes, for non-negative integer $a$ the matrix is always invertible, as can be seen from the determinant and from its expansion formula. | |
| Jul 26, 2017 at 11:59 | comment | added | valle | +1 Oh you are correct. I had a typo in the program I wrote to test this. Sorry :) ... This shows that the determinant is always positive, so the matrix is always invertible. | |
| Jul 26, 2017 at 11:50 | comment | added | G Cab | @becko before posting, I tested both formulas for various values and are both ok. In particular for $a=1$ and $h=1$, the det. should in fact be $1/8$ and the last formula gives $2/(4 \cdot1) \cdot 4/(8 \cdot 2) = 1/8)$. | |
| Jul 25, 2017 at 23:37 | review | First posts | |||
| Jul 26, 2017 at 0:52 | |||||
| Jul 25, 2017 at 23:35 | history | answered | G Cab | CC BY-SA 3.0 |