Timeline for Elementary linear algebra over a (possibly skew) field $K$
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Feb 21, 2016 at 7:33 | history | edited | Duchamp Gérard H. E. | CC BY-SA 3.0 |
Improved formatting and spelling
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| Feb 21, 2016 at 6:42 | history | edited | Duchamp Gérard H. E. | CC BY-SA 3.0 |
added "A bit on the relation between right-left kernels-images"
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| Feb 21, 2016 at 6:36 | history | edited | Duchamp Gérard H. E. | CC BY-SA 3.0 |
added "A bit on the relation between right-left kernels-images"
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| Feb 20, 2016 at 22:04 | history | edited | Duchamp Gérard H. E. | CC BY-SA 3.0 |
Improved formatting and spelling
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| Feb 20, 2016 at 16:47 | vote | accept | Drike | ||
| Feb 20, 2016 at 16:47 | |||||
| Feb 20, 2016 at 12:57 | history | edited | Duchamp Gérard H. E. | CC BY-SA 3.0 |
Added more hints and the explicit inverse of $M$
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| Feb 20, 2016 at 12:54 | comment | added | Duchamp Gérard H. E. | @SebastianGoette Of course, I had seen the ACL comments, but I wanted to give an explicit example. | |
| Feb 20, 2016 at 12:50 | history | edited | Duchamp Gérard H. E. | CC BY-SA 3.0 |
Added more hints and the explicit inverse of $M$
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| Feb 20, 2016 at 12:28 | comment | added | Duchamp Gérard H. E. | No, do not be confused because this does not invalidate your arguments and my warning is just to prevent people to treat lightheartedly rank notions. I'll put more hints in my answer. | |
| Feb 20, 2016 at 11:08 | comment | added | Sebastian Goette | I am confused now. Why would you consider columns as a left vector space at all? I also don't think that the arguments in my answer below fail for your matrix, call it $A$. The image of $A$ acting from the right on row vectors is spanned by the rows viewed as a left vector space, and they are linearly independent, so the row rank is 2. The image of $A$ acting on columns from the left is spanned by the columns, viewed as a right vector space, and has dimension 2 again. If you transpose the matrix, both ranks become 1. So we learn that transposition is dangerous, see @ACL s comment on my answer. | |
| Feb 20, 2016 at 9:13 | history | edited | Duchamp Gérard H. E. | CC BY-SA 3.0 |
Improved the aesthetics of the example
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| Feb 20, 2016 at 8:16 | history | edited | Duchamp Gérard H. E. | CC BY-SA 3.0 |
Added a warning about the rank (this question is very interesting)
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| Feb 18, 2016 at 18:09 | history | edited | Duchamp Gérard H. E. | CC BY-SA 3.0 |
improved the answer
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| Feb 18, 2016 at 17:44 | history | answered | Duchamp Gérard H. E. | CC BY-SA 3.0 |