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# Gradient Vector Field watch

1. Find the gradient vector field of the scalar field f:R^3->R

f(x) = x^TAx for A belonging to R^3x3

(x^T means x transpose)

Thanks.
2. (Original post by Joseppi)
Find the gradient vector field of the scalar field f:R^3->R

f(x) = x^TAx for A belonging to R^3x3

(x^T means x transpose)

Thanks.
Multiply out the expression using a general matrix aij

f(x) = a11x2 + a22y2 + a33z2 + (a12 + a21)xy + (a13 + a31)xz + (a23 + a32)yz
so

(2a11x + (a12 + a21)y + (a13 + a31)z)
(2a22y + (a12 + a21)x + (a23 + a32)z)
(2a33z + (a13 + a31)x + (a23 + a32)y)

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