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songCalculus

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Hi, I have a question about doing derivative with respect to a vector, can someone help please.

Problem:

Suppose A is a (nxn) dimensional symmetric matrix, [tex]\vec{x}[/tex] is a (nx1) column vector.

We know that

[tex]\frac{d A\vec{x}}{d \vec{x}}=A[/tex]

and

[tex]\frac{d \vec{x}^TA\vec{x}}{d \vec{x}}=2A\vec{x}[/tex] ( A is symmetric)

question:

[tex]\frac{d \vec{x}^TA}{d \vec{x}}=?[/tex]

many thanks in advance!

Problem:

Suppose A is a (nxn) dimensional symmetric matrix, [tex]\vec{x}[/tex] is a (nx1) column vector.

We know that

[tex]\frac{d A\vec{x}}{d \vec{x}}=A[/tex]

and

[tex]\frac{d \vec{x}^TA\vec{x}}{d \vec{x}}=2A\vec{x}[/tex] ( A is symmetric)

question:

[tex]\frac{d \vec{x}^TA}{d \vec{x}}=?[/tex]

many thanks in advance!

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