Cartesian tensor
![Two different 3d orthonormal bases: each basis consists of unit vectors that are mutually perpendicular.](/Images/godic/202501/03/Rectangular_coordinate_systems_index_lowered.svg2215.png")
![The same position vector x represented in two 3d rectangular coordinate systems each with an orthonormal basis, the cuboids illustrate the parallelogram law for adding vector components.](/Images/godic/202501/03/Rectangular_coordinate_system_position_vector_index_lowered.svg2215.png")
![Top: Angles from the xi axes to the xi axes. Bottom: Vice versa.](/Images/godic/202501/03/Rectangular_coordinate_systems_angles_index_lowered.svg2215.png")
![Cyclic permutations of index values and positively oriented cubic volume.Anticyclic permutations of index values and negatively oriented cubic volume.Non-zero values of the Levi-Civita symbol εijk as the volume ei · ej × ek of a cube spanned by the 3d orthonormal basis.](/Images/godic/202501/03/Epsilon_volume_cyclic_permutations.svg2215.png")
In geometry and linear algebra, a Cartesian tensor uses an orthonormal basis to represent a tensor in a Euclidean space in the form of components. Converting a tensor's components from one such basis to another is through an orthogonal transformation.