I've been working on this problem lately where I've been looking at the second derivatives of 2D and 3D density fields. Now, the second derivatives of the field can be represented in a matrix, which can be thought of as an N-dimensional ellipse with the principal axes aligned along some angle in which the second derivative matrix is diagonal.(adsbygoogle = window.adsbygoogle || []).push({});

Anyway, I've solved the full problem in 2D (angle and all), but in 3D, I've only been able to diagonalize the matrix. I haven't yet figured out how to determine the angle that represents. Does an easy analytic solution exist for this or will I have to resort to numerical guesstimations?

**Physics Forums - The Fusion of Science and Community**

# Diagonalizing a 3x3 second derivative matrix

Know someone interested in this topic? Share a link to this question via email,
Google+,
Twitter, or
Facebook

Have something to add?

- Similar discussions for: Diagonalizing a 3x3 second derivative matrix

Loading...

**Physics Forums - The Fusion of Science and Community**