Question

Let's play around with matrix derivatives! A trace Tr(X)Tr(X) of a matrix XX is a sum of its diagonal elements. For example: Tr\left( 1331 \right) = 1 + 1 = 2Tr( 1 3 ​ 3 1 ​ )=1+1=2. Note that trace is a scalar! Let's find a matrix notation for \frac{\partial Tr(X^2)}{\partial X} ∂X ∂Tr(X 2 ) ​ for matrix X = \left( x1,1x2,1x1,2x2,2 \right)X=( x 1,1 ​ x 2,1 ​ ​ x 1,2 ​ x 2,2 ​ ​ ), where X^2X 2 is a matrix product X \cdot XX⋅X. Please do this element-wise and figure out a matrix notation for it:

Answer 1

What is this??????

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Answer 2

Answer:

2X.T

Explanation: