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Derivative of a Constant Matrix

  1. Jul 9, 2013 #1
    Let's suppose we have a matrix ##\textbf{C}=\begin{bmatrix}c_{1,1} & c_{1,2} & c_{1,3} & \cdots & c_{1,m} \\ c_{2,1} & c_{2,2} & c_{2,3} & \cdots & c_{2,m} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ c_{n,1} & c_{n,2} & c_{n,3} & \cdots & c_{n,m}\end{bmatrix}##, such that ##\forall i,j\in\mathbb{Z}:1 \leq i \leq n, 1 \leq j \leq m, \, \frac{\partial c_{i,j}}{\partial x}=0##. In other words, a constant matrix.

    Is ##\frac{d\textbf{C}}{dx}## equal to 0 or the nxm 0-matrix? I thought it was the latter of the two, but I was thinking about it today and I wasn't sure.
  2. jcsd
  3. Jul 9, 2013 #2


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    Gold Member

    Definitely the latter. Just think of the way differentiation works for vectors: component-wise. Then jack the dimension up by one to get matrices, and you'll see that it still works the same way.
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