Does $\textbf{a}\cdot\textbf{b}=\textbf{a}^T\textbf{b}$?

Question

From this question, does $\textbf{a}\cdot\textbf{b}=\textbf{a}^T\textbf{b}$?

Answer 1

Assuming $\mathbf a$ and $\mathbf b$ are column vectors, then yes.

The transpose of a column vector is a row vector.

Then the identity trivially follows from the definitions of transpose and matrix product.