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I know the definition of the Jacobian and hessian of $x$. However, I am confused how to find the jacobian and hessian of $z=Ax+b$. $A$ is an $m\times n$ matrix and b is a $m\times 1$ vector.

Hessian matrix of a vector-valued function is a third order tensor of the form: $H(z)=[H(f1) H(f2) \dots H(fm)]$

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    What do you mean by the gradient of a vector valued function? That is nonstandard terminology. – 2017-02-12
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    changed it to jacobian @littleO – 2017-02-12
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    Now a follow-up question, what do you mean by the Hessian of a vector valued function? – 2017-02-12
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    In your definition of the Hessian, are you assuming that $f$ is a scalar-valued function? If so, then this definition does not apply to your vector-valued function $z$. – 2017-02-12
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    @littleO I have edited my post. – 2017-02-12

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