Taking derivative of a transposed matrix

In summary, the conversation is about taking the derivative of a matrix (z-m1)^T with respect to m, where z is an n x n matrix and 1 is an n x 1 column vector. The derivative is calculated to be (z-1)^T, with a correction made by another participant.
  • #1
MaxManus
277
1
I have a matrix (z-m1) ^T where z is a matrix and 1 i a column where all the elements are 1. Can anyone help me with taking the derivative with respect to m?

T is for transpose.
 
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  • #2
MaxManus said:
I have a matrix (z-m1) ^T where z is a matrix and 1 i a column where all the elements are 1. Can anyone help me with taking the derivative with respect to m?

T is for transpose.

z-m1 doesn't make sense to me. I'm assuming that z is an n x n matrix and 1 is an n x 1 matrix (column vector), so the subtraction is undefined.
 
  • #3
Thanks, I assumed z to be an n x n matrix as well but since that doesn't make any sense it must be a n*1 matrix and then I can just use ordinary derivation and I get

(z-1)^T
 
  • #4
I think it would be -1T, where 1 is as you defined it.
 
  • #5
Yes of course, thanks
 

Related to Taking derivative of a transposed matrix

1. What is a derivative of a transposed matrix?

A derivative of a transposed matrix is the rate of change of the elements of the matrix with respect to a given variable. It is a way to measure the sensitivity of the matrix to changes in the variable.

2. How is the derivative of a transposed matrix calculated?

The derivative of a transposed matrix is calculated by taking the derivative of each element in the matrix and then transposing the resulting matrix. This can be done using the rules of matrix calculus.

3. What is the significance of taking the derivative of a transposed matrix?

Taking the derivative of a transposed matrix can help us understand how the elements of the matrix are affected by changes in the variable. This can be useful in many fields such as physics, economics, and engineering.

4. Can any matrix be transposed and have a derivative?

Yes, any matrix can be transposed and have a derivative as long as the elements of the matrix are differentiable functions of the variable.

5. Are there any special properties of the derivative of a transposed matrix?

Yes, one special property is that the derivative of a transposed matrix is equal to the transpose of the derivative of the original matrix. This is known as the transpose rule and can be proven using the rules of matrix calculus.

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