Efficiently Calculating Determinants Using Cofactors and Expansion

  • Context: Graduate 
  • Thread starter Thread starter lo2
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the calculation of determinants using cofactor expansion and the notation involved in expressing these calculations. Participants explore the clarity of the original question and the mathematical expressions presented.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant proposes a summation notation for the determinant, questioning if it can be expressed in a simplified form.
  • Another participant seeks clarification on the notation used, particularly the meaning of \( a'_{rs} \) and the intent behind the original question.
  • Some participants agree that the summation does indeed expand to the long-hand version of the determinant, but express confusion about the relevance of determinants to the question posed.
  • There is a request for clearer communication in the original post, emphasizing the importance of complete sentences for understanding.
  • A participant expresses frustration over the clarity of their own post and requests deletion of their contribution, leading to a discussion about the deletion process on the forum.

Areas of Agreement / Disagreement

Participants generally agree that the summation notation is equivalent to the expanded form of the determinant, but there is disagreement regarding the clarity of the original question and the definitions used. The discussion remains unresolved regarding the intent and clarity of the initial post.

Contextual Notes

The discussion highlights limitations in the clarity of notation and communication, which may affect understanding. There are unresolved questions about the definitions and implications of the terms used in the original post.

lo2
Can this be written.

[tex] \[<br /> \det{\textbf{A}}=a_{11}a'_{11}+a_{12}a'_{12}+\ldots+a_{1n}a'{1n}<br /> \]<br /> [/tex]

As. (Where I just use p instead of n for obvious reasons)

[tex] \[<br /> \sum^{n}_{p=1}{a_{1p}a'_{1p}}<br /> \][/tex]

Since.

[tex] \[<br /> a'_{ij}=(-1)^{i+j}(\det{\textbf{A}_{ij}})<br /> \][/tex]

And yes we are talking determinants.
 
Last edited by a moderator:
Physics news on Phys.org
Come on please help, would be most appreciated.
 
If you want help then write in a clear manner that people can understand, preferably in complete sentences - if people have to work hard at understanding what the question is they will tend not to bother working out what you intend.

What is a'_{rs}? What are you trying to prove?

I suspect that that doesn't matter. If all you're asking is does that summation expand to give the long hand version, then the answer is 'yes'. Just write down what the summation means.

Det has nothing to do with it as far as I can tell. But because you made a big point of saying it was abuot Det I have no idea if I've answered the question you intended to ask.
 
lo2 said:
[tex]a_{11}a'_{11}+a_{12}a'_{12}+\ldots+a_{1n}a'_{1n} = \sum^{n}_{p=1}{a_{1p}a'_{1p}}[/tex]

yes, these are equal.

Note, I cleaned up your latex. There is no need to include a \[ inside tex tags - I don't think it does anything.
 
I do think I made myself very clear, but well anyway thank you for the help!
 
Could this post please be deleted.
 
You can delete it yourself.

If you think you were clear, can I ask what you think A_{ij} is? 'Cos we don't have a clue. And the 'since' is completely misleading. As is the sentence structure ('As.' is not a sentence, and is confusingly, given the post, like a plural form of A).
 
matt grime said:
You can delete it yourself.

How to do that?
 
It's too late now, but next time click on 'edit' and there is an option to delete. The edit option vanishes after some amount of time.
 
  • #10
But I would really like to get this post deleted.
 
  • #11
Why? (added junk to meet minimum post requirement)
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 15 ·
Replies
15
Views
5K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 15 ·
Replies
15
Views
4K
  • · Replies 21 ·
Replies
21
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K