Matrix. Calculation

Question

matrix $$U=\begin{bmatrix} a &b & c &d &e \\ f& j& h & f & a\\ e&r &t &g &n \\ f& h& v& b &m \\ e& r & t &y &n \end{bmatrix} $$

what means U(:,1) and U(:,1:3)?

Answer 1

In Matlab notation, $U(:,1)$ means the first column of $U$.

$U(:,1:3)$ means the submatrix of $U$ that consists of the first $3$ columns.

Answer 2

$U(:,1)$ = first column of $U$ \begin{bmatrix} a & \\ f& \\ e& \\ f& \\ e& \end{bmatrix} U(:,1:3) = first three columns of $U$\begin{bmatrix} a &b & c \\ f& j& h \\ e&r &t \\ f& h& v\\ e& r & t \end{bmatrix}