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Question: Let z = ||Ax - b||2. Show that
(∂z/∂x) = 2ATAx - 2ATb.
Use z = (Ax - b)T (Ax - b).
We can also consider the second derivative of z = f(x), which is the Hessian matrix of z with entries
H = ∂2z/∂x2 = ∇2f(x)
Hmn = ∂2z/∂xm∂xn
If the entries of the vector z = (z1, ..., zM)T are real-valued functions of the vector x, the derivative of z is the matrix whose mth column is the derivative of the real-valued function zm. This matrix is usually called the Jacobian matrix of z. If M = N the determinant of the Jacobian matrix is the Jacobian.
Prepare a Flexible Budget Gator Divers is a company that provides diving services such as underwater ship repairs to clients in the Tampa Bay area.
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