So I have a quick question that will hopefully yield some clarification. So the divergence of a dyadic ##\bf{AB}## can be written as,(adsbygoogle = window.adsbygoogle || []).push({});

$$\nabla \cdot (\textbf{AB}) = (\nabla \cdot \textbf{A}) \textbf{B} + \textbf{A} \cdot (\nabla \textbf{B})$$

where ##\textbf{A} = [a_1, a_2, a_3]## and ##\textbf{B} = [b_1, b_2, b_3]##. However, it seems to me that the first term of the identity yields a vector (the vector ##\bf{B}## scaled by the divergence of ##\bf{A}##), while the second term yields a scalar. Since one cannot simply add a scalar quantity to a vector quantity, it would appear the identity is false, or perhaps I am missing something. I know the dyadic of ##\bf{AB}## yields a tensor, and the divergence of a tensor is a vector, but it doesn't appear that the second term on the right hand side of the identity is a vector. Any help would be greatly appreciated.

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

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

# I Vector Calculus?

Tags:

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - Vector Calculus | Date |
---|---|

I Question about vector calculus | Aug 11, 2017 |

I Proofs of Stokes Theorem without Differential Forms | Jan 24, 2017 |

I Kronecker Delta and Gradient Operator | Jan 8, 2017 |

I Vector Calculus: What do these terms mean? | Dec 2, 2016 |

I Find potential integrating on segments parallel to axes | Nov 17, 2016 |

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