Math Is Fun Forum

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Derivative of a matrix

The derivative of a matrix is the matrix containing the derivative of each entry. I thought this was by definition but it is not.

From the above definition of the derivative of a matrix, how do I derive that:

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Derivative of a matrix

What is X?

It looks to me like you're trying to define the derivative of a n to m dimensional function, but this doesn't make sense because you say that I is an interval.  So maybe you are attempting to define the derivative of a path?

Either way, please remember that there is no such thing as a derivative of a matrix.  A derivative of a function can be represented by a matrix, but this is still a derivative of a function.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: Derivative of a matrix

The definition I gave above is copied from the booklet word by word. Then there's a side exercise to show what I asked by the above definition.

Last edited by LuisRodg (2009-08-05 13:18:16)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Derivative of a matrix

Huh, weird, but I guess it's ok.  I've never heard of derivatives talk about in this way.

Just write the entire thing out.  Fix an i and j, and in terms of a_ij, what is A(t) - A(gamma)?  And then what is this when it is divided by t - gamma?

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

juriguen

Member

Registered: 2009-07-05

Posts: 59

Re: Derivative of a matrix

Hi!

According to what you write, you're defining an element wise derivative, after all!

I would say:

Jose

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“Make everything as simple as possible, but not simpler.” -- Albert Einstein