# Tensor and Matrix order

## Tensor Notation

All symmetric tensors in IMPETUS Solver uses an alternative notation of the Voigt notation.

\( \begin{bmatrix} \sigma_{1} & \sigma_{6} & \sigma_{5} \\ & \sigma_{2} & \sigma_{4} \\ & & \sigma_{3} \end{bmatrix} \) Traditional voigt notation: `11, 22, 33, 23, 13, 12`.

\( \begin{bmatrix} \sigma_{1} & \sigma_{4} & \sigma_{6} \\ & \sigma_{2} & \sigma_{5} \\ & & \sigma_{3} \end{bmatrix} \) Our definition is: `11, 22, 33, 12, 23, 13`.

## Matrix access order

Matrices are stored in column major order.

\( \begin{bmatrix} \sigma_{11} & \sigma_{12} & \sigma_{13} \\ \sigma_{21} & \sigma_{22} & \sigma_{23} \\ \sigma_{31} & \sigma_{32} & \sigma_{33} \end{bmatrix} \) The order of the matrix is: `11, 21, 31, 12, 22, 32, 13, 23, 33`