Coordinate Vector

A coordinate vector is denoted as a vector comprised of coefficients of the basis vector.

• Let $\beta =\{v_1,\dots ,v_n\}$
• For any vector in $v\in V$
• Where $v=b_1{v}_1+\cdots +b_n{v}_n$

\left[\begin{array}{c} b_{1} \ \vdots\ b_{n} \end{array}\right]

# Example Write $v = (2,0)$ with respect to $\alpha = \{ (1,0),(0,1) \}$ - $v = 2(1,0) + 0(0,1)$ - Thus, $$[v]_{\alpha} = \left[\begin{array}{c} 2 \\ 0 \end{array}\right]