Notation for Vector Transpose: \mathbf v

[Niles]

Homework Statement

Hi guys

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

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

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 &amp; 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 &amp; x_2 \end{pmatrix} \begin{pmatrix} y_1 \\ y_2 \end{pmatrix}

 

[Niles]

Thanks!