## 2.24Summary of tensor algebra

Below is tensor algebra applied to Cartesian () co-ordinates using: scalar ; vectors , ; tensors , , .

### Products

• Inner product of two vectors, Sec. 2.3
• Outer product of two vectors, Sec. 2.8
• Inner product of vector and tensor, Sec. 2.6
• Inner product of two tensors, Sec. 2.8
• Double inner product of two tensors, Sec. 2.17
• Cross product of two vectors, ﬁrst used in Sec. 3.3 , produces a vector with components  (2.70)

### Tensors and operations

• Transpose of a tensor, Sec. 2.7
• Symmetric and skew tensors, Sec. 2.7
• Trace of a tensor, Sec. 2.10
• Identity tensor, Sec. 2.8
• Deviatoric and spherical tensors, Sec. 2.10
Notes on CFD: General Principles - 2.24 Summary of tensor algebra