Taking derivative of a transposed matrix

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    Derivative Matrix
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Homework Help Overview

The discussion revolves around taking the derivative of a transposed matrix expression involving a matrix \( z \) and a column vector of ones. Participants are trying to clarify the dimensions and definitions of the matrices involved.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the dimensionality of the matrices involved, questioning the validity of the subtraction operation between \( z \) and the column vector of ones. There is a discussion about whether \( z \) is an \( n \times n \) matrix or an \( n \times 1 \) matrix.

Discussion Status

Some participants have provided insights into the dimensionality of the matrices, leading to a reconsideration of the original expression. There is an acknowledgment of the need for clarity regarding the definitions of \( z \) and the column vector of ones.

Contextual Notes

There is uncertainty regarding the dimensions of the matrices involved, which affects the interpretation of the derivative operation. Participants are navigating the implications of these assumptions on the problem at hand.

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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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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.
 
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
 
I think it would be -1T, where 1 is as you defined it.
 
Yes of course, thanks
 

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