Talk:Characteristic polynomial

Secular function section
This section is completely incomprehensible to me. What on earth is "matrix tearing and gruing" and "determinant of a matrix with a shift"? Where do the poles of the secular function come from? A polynomial has no poles.

Most of this section looks like something from uncyclopedia and is completely confusing. I doubt it belongs on this page at all. HugoBarnaby (talk) 08:55, 20 October 2010 (UTC)


 * I agree. Everything after the first paragraph, particularly the middle of this section, is very poorly written. I can only assume it was written by a non-native speaker of English or, like you said, as a joke. It would be great if someone familiar with secular functions could re-write this section more clearly. 155.41.17.62 (talk) 18:42, 14 October 2011 (UTC)

Note that the source 10 "secular equation". Retrieved January 21, 2010. is down. — Preceding unsigned comment added by Anonime17 (talk • contribs) 13:11, 16 December 2020 (UTC)

Overhaul needed
Article mentions two conventions, justifies settling on one, then uses the other in the tail of the article. Perhaps settle on one convention (the one argued for at the beginning) used throughout except in one section which explains the other, gives corresponding forms, show how to interconvert, so that all "alternative" convention is restricted to that section.

An explicit expansion of the polynomial (with the alternative form in the "alternative" section) showing the terms/coefficients referred to later might help clear things up. — Preceding unsigned comment added by 70.72.144.66 (talk) 17:13, 8 May 2013 (UTC)

$$\bigwedge$$ instead of $$\Lambda$$?
In the entry text I read:

"$$ p_A (t) = \sum_{k=0}^n t^{n-k} (-1)^k \operatorname{tr}(\Lambda^k A) $$"

After consulting the entry about exterior algebra (which is referred to by the text), I noticed that the symbol $$\bigwedge$$ is used there.

Is this actually the symbol that was intended / should be used instead of capital lambda in the current entry?Redav (talk) 13:42, 28 November 2020 (UTC)

Characteristic of what?
The current entry text contains:

"When the characteristic is 0 it may alternatively be computed as a single determinant, that of the k×k matrix, [...]"

Could someone tell us the characteristic of what is meant here? (I did follow the link to "characteristic" (algebra) but that seems to deal with rings and fields, and the connection to the quoted statement is not clear to me.Redav (talk) 14:01, 28 November 2020 (UTC)
 * The connection is that the facor 1/k! makes no sense in non-zero characteristice. However I have edited the article for clarification. D.Lazard (talk) 14:43, 28 November 2020 (UTC)
 * Thanks a lot! I consider that helpful.Redav (talk) 16:17, 29 November 2020 (UTC)

Notation
This article uses p_A(t), but I’ve also seen \chi_A(t). Perhaps a brief note on common notations is needed. TomFryers (talk) 16:18, 14 February 2021 (UTC)
 * AFIK, there is commonly accepted notation. D.Lazard (talk) 16:24, 14 February 2021 (UTC)