Talk:Minor (linear algebra)

Confused

A k×k minor of A is the determinant of a k×k matrix obtained from A by deleting m-k rows and n-k columns.

I'm a little confused now; I'm guessing doing this makes sure that when you take a minor you always get a square matrix so taking the determinant makes sense, but how can this be related to the M_ij notation I have seen everywhere? (And where in the matrix are we deleting these rows and columns from?) Dysprosia 00:57, 1 Nov 2003 (UTC)

The indices i and j have to range over subsets I of {1,2,...,m} and J of {1,2, ...,n}, each of size k. We get a minor for each good choice of I and J. Charles Matthews 11:31, 1 Nov 2003 (UTC)

intro to cofactors

I really don't think starting with an example is the best way to write this article. The general definition of a cofactor should be written first, and examples later. After looking harder, this page seems to be mostly two examples, rather than explanation of general treatment. This needs to be fixed, but I don't know enough to fix it. Fresheneesz 23:16, 4 February 2006 (UTC)

It's not really appropriate to put "use a f****** header" above comments when headers were not convention on Talk. It's not really appropriate to use that sort of language on Talk in any case. It is probably possible to write a symbolic definition in the general case, but this would not be very illustrative, and the current explanation does enough to explain what a minor or cofactor is generally. Dysprosia 23:49, 4 February 2006 (UTC)

Merge

Since the minor and cofactor only differ by a sign, there's really no reason to have two articles. I think having a cofactor section in the minor article (as is currently the case) is the best way to go, and redirect cofactor there. I might even be in favour of merging both into the determinant article. Mark M (talk) 09:22, 1 April 2013 (UTC)

Undefined notation

The section Cofactor as the derivative of the determinant of second-order tensor begins as follows:

"For any invertible second-order tensor A the following identity holds:

$${\frac {\partial {\text{ det}}\left(\mathbf {A} \right)}{\partial \mathbf {A} }}={\text{det}}\left(\mathbf {A} \right)\mathbf {A} ^{-T}={\text{cof}}\left(\mathbf {A} \right)$$

which is useful in the field of nonlinear solid mechanics."

But the notation "${\text{cof}}\left(\mathbf {A} \right)$" has not been defined anywhere in this article.

I hope that someone knowledgeable about this subject can fix this.

${\text{cof}}\left(\mathbf {A} \right)$ denotes certainly the matrix of the cofactors, but the derivative with respect to a matrix and tensors are not defined/considered in this article. So, I have removed this section. D.Lazard (talk) 18:36, 28 December 2024 (UTC)