Re: Derivative of the Determinant Function

From: "david petry" <david_lawrence_petry@xxxxxxxxx>
Date: 6 May 2006 15:56:51 -0700

Corey wrote:

Hi there. If I were to compute the derivative of the determinant
function as a function of the linear space of n x n matrices, how would
I go about doing this? My initial thought was to treat this as a Hodge
duality problem, but I'm not really sure where to begin if I take this
approach. I was just wondering if anyone could offer me some input,
thanks.

I hate to answer questions when I don't really understand what the
question is, but in this case, pointing that out may be the answer.

Usually a derivative involves one scalar variable. But the linear space
of nXn matrices has dimension n^2, and hence is equivalent to n^2
scalar variables. So something is not quite right about your question.

.

Follow-Ups:
- Re: Derivative of the Determinant Function
  - From: David C . Ullrich
- Re: Derivative of the Determinant Function
  - From: Lee Rudolph

References:
- Derivative of the Determinant Function
  - From: Corey

Prev by Date: Re: Linear operators - clarification of terminology
Next by Date: Re: Yet Another Factoring Algorithm (yafa)
Previous by thread: Derivative of the Determinant Function
Next by thread: Re: Derivative of the Determinant Function
Index(es):
- Date
- Thread

Relevant Pages

Re: Derivative of the Determinant Function
... function as a function of the linear space of n x n matrices, ... scalar variables. ... (Saying f is differentiable at a point is more than saying ... all the first-order partials are continuous. ...
(sci.math)
Re: Are these results already known? If not, how to publish?
... the third space and log-log space becomes mirror images of each other through the linear space. ... The observations also find, in the initial phase, that the extent between zero and infinity is imaginary, while the zero is the only real thing. ... etc), some without dimension, some with different dimensions at different points and some with fractional dimension ...
(sci.math)
Re: Derivative of the Determinant Function
... Corey wrote: ... function as a function of the linear space of n x n matrices, ... Note that the derivative with respect to t at the value t=0 equals ... the answer to the subject line "Derivative of the Determinant ...
(sci.math)
Re: Derivative of the Determinant Function
... Corey wrote: ... function as a function of the linear space of n x n matrices, ... I think that you are asking for the derivative of the determinant at the identity matrix, that is, what is fif: ...
(sci.math)