- #1
Grufey
- 30
- 0
Hello,
I'm solving a problem in optics, and I found the next question:
Let f:\mathbb{R}^2\rightarrow\mathbb{R} be a function, such as (x,y)\rightarrow(z), which is a surface in IR^3.I need an estimator of the stability of that surface or any indicator of the inclination of the surface in a point. In other words: if in IR, the derivative indicates the variation of the function or the stability, I require another parameter that measures the variation or stability of a surface in IR^3My first thought was to use something similar to the Jacobian, but this is a matrix, not a number. I need a number. Also, I thought that the determinant of the Hessian matrix could be good enough, but I'm unsure as to what the mathematical meaning of that operation really is.
I'm solving a problem in optics, and I found the next question:
Let f:\mathbb{R}^2\rightarrow\mathbb{R} be a function, such as (x,y)\rightarrow(z), which is a surface in IR^3.I need an estimator of the stability of that surface or any indicator of the inclination of the surface in a point. In other words: if in IR, the derivative indicates the variation of the function or the stability, I require another parameter that measures the variation or stability of a surface in IR^3My first thought was to use something similar to the Jacobian, but this is a matrix, not a number. I need a number. Also, I thought that the determinant of the Hessian matrix could be good enough, but I'm unsure as to what the mathematical meaning of that operation really is.
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