- Let x=(x1,x2,...,xn) be standart coordinates of a Cartesian (n+1)-space and y=(y1,y2,...,yn) another one, where yi=aijxj, i,j=1,2,...,n.
- Denote Hess(z(x)) the Hessian of a real-valued function z=z(x1,x2,...,xn).
- We obtain that
- where A=(aij), A^{T} the transpose of A, "." matrix multiplication.
- The question is: the equality in (1) is new one? Or is well-known?
- Many thanks in advance for your interest and comments...
Patrick Erik Bradley
Assuming that A is constant, this is precisely how the Hessian behaves under linear coordinate transformations A. This is not a new result.
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Muhittin Evren Aydin
Dear Professors Bradly and Low, many thanks for your answers. I agree with both of you.
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