I'm trying to find a way of reducing a rank-3 tensor field into a matrix, but am having trouble finding a good way to do it. The situation set up is as follows:(adsbygoogle = window.adsbygoogle || []).push({});

Let's say that I have a [itex] 3\times 3[/itex] matrix and a [itex] 5 \times 1 [/itex] vector as follows

[tex] A(x) = \begin{pmatrix} a_{11}(x) & a_{12}(x) & a_{13}(x) \\ a_{21}(x) & a_{22}(x) & a_{23}(x) \\ a_{31}(x) & a_{32}(x) & a_{33}(x) \end{pmatrix}, \qquad \qquad x = \begin{pmatrix} x_1 \\ x_2\\ x_3 \\ x_4 \\ x_5 \end{pmatrix} [/tex]

Now I want to find a tangent plane to a surface defined by A(x) at some point [itex] \bar x [/itex] to create some constraints, namely, I want to do something of the form

[tex] \nabla A(x) (x - \bar x) = 0 [/tex]

Now the problem here is that [itex] \nabla A(x) [/itex] is a rank 3 tensor. I need to find some what of ''matricizing'' this tensor into a matrix so that I can solve a linear programming problem with it. Any ideas?

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

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Reducing to a matrix

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads for Reducing matrix | Date |
---|---|

SVD of a reduced rank matrix still has non-zero U and V`? | Apr 29, 2015 |

Reduced row echelon form of a square matrix | Nov 12, 2012 |

Row reducing the matrix of a linear operator | Jun 6, 2011 |

If a mxn matrix A, m>=n has a reduced QR-decomposition | Sep 15, 2010 |

Reduced row echelon form of matrix | Sep 26, 2005 |

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