Matrix Derivation: 2x1 A and B with Dimension and dA/dB Calculation

In summary, the conversation discussed finding the derivative of matrix A with respect to matrix B, and the resulting Jacobian matrix. It was also mentioned that the question about finding a formula for the derivative of XTATAX with respect to A should be posted in a separate thread, as it may be considered a homework question.
  • #1
tommyhakinen
36
0
Hi,

I need help with matrix derivation. I have 2 matrices of dimension 2x1, A and B.
A = [f(x) x][tex]^{T}[/tex]
B = [y x][tex]^{T}[/tex]

I would like to find the dA/dB. How do I do this? and what is the dimension of the resultant matrix?
 
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  • #2
What is the function that you want to take the derivative of?
 
  • #3
[tex]\frac{D(A)}{D(B)}=\left(\begin{array}{cc}\frac{\partial f(x)}{\partial y}&\frac{\partial f(x)}{\partial x}\\\frac{\partial x}{\partial y}&\frac{\partial x}{\partial x}\end{array}\right)=\left(\begin{array}{cc}0&f^\prime\\0&1\end{array}\right)[/tex]

This should be it if I'm not mistaken. What you're asking is basically the Jacobian matrix of a vector-valued function [tex]g(y,x)=(f(x),x)[/tex]
 
  • #4
batboio said:
[tex]\frac{D(A)}{D(B)}=\left(\begin{array}{cc}\frac{\partial f(x)}{\partial y}&\frac{\partial f(x)}{\partial x}\\\frac{\partial x}{\partial y}&\frac{\partial x}{\partial x}\end{array}\right)=\left(\begin{array}{cc}0&f^\prime\\0&1\end{array}\right)[/tex]

This should be it if I'm not mistaken. What you're asking is basically the Jacobian matrix of a vector-valued function [tex]g(y,x)=(f(x),x)[/tex]

thank you very much. that helped a lot.
 
  • #5
please help me about this quastion :
suppse A be a square matrix and X be a coln matrix AT and XT are their transpos matrices find a formula for this derivative :
d XTATAX/ dA
 
  • #6
Please create a new thread for your question. And if it is homework, it belongs in the homework forums.
 

1. What is a matrix?

A matrix is a collection of numbers arranged in rows and columns. It is a mathematical tool used to represent and manipulate data in various fields such as mathematics, physics, and engineering.

2. What is the purpose of deriving a matrix?

The purpose of deriving a matrix is to simplify and condense complex data into a more manageable and organized form. It allows for efficient computation and analysis of the data.

3. How is a matrix derived?

A matrix is derived by applying mathematical operations such as addition, subtraction, multiplication, and division to the elements of the original matrix. The resulting matrix will have the same dimensions as the original matrix.

4. What are the different types of matrix derivation?

There are several types of matrix derivation, including scalar multiplication, matrix addition and subtraction, matrix multiplication, and matrix inversion. Each type serves a different purpose and is used in various applications.

5. What are some real-world applications of matrix derivation?

Matrix derivation is used in a variety of fields, such as computer graphics, statistics, economics, and physics. It is also used in linear algebra to solve systems of equations and in machine learning for data analysis and pattern recognition.

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