Can the matrix be differentiated with respect to a vector

[sainistar]

Hello Mathematician

Can the matrix be differentiated with respect to a vector?

Regards
Aman

 

[kai_sikorski]

This might be of some help to you

http://en.wikipedia.org/wiki/Tensor_derivative_(continuum_mechanics)#Gradient_of_a_tensor_field

A 2nd-order tensor and a matrix are basically the same thing.

 

[HallsofIvy]

I would phrase that differently. A matrix can be used to represent a tensor, in the same sense that a list of numbers represents a vector- but they are not "the same thing", even basically.

sainistar, if your given matrix is a function of a vector, then you can certainly differentiate.

 

[Bacle2]

Have you searched thru some of the basics:

http://en.wikipedia.org/wiki/Matrix_calculus

or:

http://math.stackexchange.com/questions/94562/matrix-vector-derivative


or:

http://math.stackexchange.com/questions/100174/differentiating-a-function-with-respect-to-a-vector

 

[blue_raver22]

Yes, it is possible to differentiate a matrix with respect to a vector. This is known as the Jacobian matrix, which is a matrix of partial derivatives of a vector-valued function. It is often used in multivariable calculus and optimization problems to find the rate of change of a vector function with respect to its input parameters. However, the result of differentiating a matrix with respect to a vector will also be a matrix, not a vector. So while it is possible, the end result may not be what you were expecting. I hope this helps clarify your question.