Exploring the Matrix Version of the Multivariable Chain Rule

In summary, The conversation is about the matrix version of the chain rule and the person is looking for websites or resources to learn about it. They clarify that they are looking for the multivariable version and mention applying the chain rule to each component separately. They also mention potential questions they may have while learning about it.
  • #1
Benny
584
0
Hi, does anyone know of any websites which have some theory and perhaps some examples of the matrix version of the chain rule. Neither of the books I have covers this particular topic so I'd like to read up on it. Any help would be appreciated thanks.
 
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  • #2
I'm not quite sure what you're asking for.

If you have a function with several terms (ax^2 + bx + c, for example), you apply the chain rule to each term separately. If you have a vector, you apply the chain rule to each component separately. If you have a matrix, you apply the chain rule to each element separately.
 
  • #3
I would think OP is referring to the multivariable version of the chain rule.
 
  • #4
I should've made it more clear that I was referring to the multivariable chain rule. I've managed to find something about it and I might post some questions if I find some I can't work out. Thanks anyway.
 

FAQ: Exploring the Matrix Version of the Multivariable Chain Rule

What is the matrix version of chain rule?

The matrix version of chain rule is a mathematical concept that is used to find the derivative of a composition of functions in the form of matrices. It is an extension of the traditional chain rule in calculus.

Why is the matrix version of chain rule important?

The matrix version of chain rule is important because it allows us to find the derivative of complex functions involving matrices, which are commonly used in many scientific fields such as physics, engineering, and computer graphics.

How is the matrix version of chain rule calculated?

The matrix version of chain rule is calculated by multiplying the derivative of the outer function with the derivative of the inner function. This process is repeated until the desired derivative is obtained.

What are some applications of the matrix version of chain rule?

The matrix version of chain rule is used in various applications such as gradient descent in machine learning, calculating the motion of rigid bodies in physics, and analyzing the stability of systems in control theory.

Are there any limitations to the matrix version of chain rule?

One limitation of the matrix version of chain rule is that it can only be applied to functions that are differentiable. It also requires a good understanding of linear algebra and matrix operations, which can be challenging for some individuals.

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