eigensteve
commented
3 years ago Thanks Juan Pablo — this is a really good catch! I actually just fixed this for the second edition of the book, so hopefully it is right soon. Thanks for the note, and please feel free to send me any other comments/typos directly.
Best wishes, Steve
On Sep 13, 2021, at 5:35 PM, Juan Pablo Carbajal @.***> wrote:
Hi, I couldn't find any other way to communicate with the authors of the book. Please excuse me for using this way. Also I couldn't find an errata for the book, which i think it would be great to have in the website of the book. My observation here is that the use of full column rank in the book, pp. 16 are not correct. A shirt-fat matrix cannot have full column rank by definition. Since rank(A) <= min(n,m) and in this case n<<m, the rank is at most n, which is the row rank. So a short-fat matrix is likely to have full row rank, not full column rank (number of linearly independent columns equals number of columns), as stated in the book. In the same page it is also said that a tall-skinny matrix cannot have full column rank, when indeed this is the likely scenario. I suspect that the authors are using a non-conventional definition of full column rank that they forgot to define. The conventional definition is intuitive and consistent: column rank == number of linearly independent columns, hence full column rank means all columns are linearly independent.
Regards
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kakila
Hi, I couldn't find any other way to communicate with the authors of the book. Please excuse me for using this way. Also I couldn't find an errata for the book, which i think it would be great to have in the website of the book. My observation here is that the use of full column rank in the book, pp. 16 are not correct. A shirt-fat matrix cannot have full column rank by definition. Since rank(A) <= min(n,m) and in this case n<<m, the rank is at most n, which is the row rank. So a short-fat matrix is likely to have full row rank, not full column rank (number of linearly independent columns equals number of columns), as stated in the book. In the same page it is also said that a tall-skinny matrix cannot have full column rank, when indeed this is the likely scenario. I suspect that the authors are using a non-conventional definition of full column rank that they forgot to define. The conventional definition is intuitive and consistent: column rank == number of linearly independent columns, hence full column rank means all columns are linearly independent.
Regards