Notation for Vector Transpose: \mathbf v

[Niles]

Homework Statement

Hi guys

If I have a vector v, then is it correct notation to write

$$\mathbf v = \left( {\begin{array}{*{20}c} {v_1 } \\ {v_2 } \\ \end{array}} \right) = (v_1,v_2)^T,$$

where ^T is the transpose?

 

[Rasalhague]

Yes. Although you can write a vector as either a row or a column, the usual convention is to treat the column form as more basic:

$$x = \begin{pmatrix} x_1\\ x_2 \end{pmatrix}$$

$$x^T = \begin{pmatrix}x_1 & x_2 \end{pmatrix}$$

so that the dot product $\textbf{x} \cdot \textbf{y}$ is usually expressed in matrix form as

$$x^T y = \begin{pmatrix}x_1 & x_2 \end{pmatrix} \begin{pmatrix} y_1 \\ y_2 \end{pmatrix}$$

 

[Niles]

Thanks!