Definition:Submatrix/Example

Definition

Let $\mathbf A$ be the $3 \times 4$ matrix defined as follows:

$\mathbf A = \begin{bmatrix}

a_{11} & a_{12} & a_{13} & a_{14} \\ a_{21} & a_{22} & a_{23} & a_{24} \\ a_{31} & a_{32} & a_{33} & a_{34} \end{bmatrix}$

Then:

$\mathbf A \left[{1, 2; 1, 3, 4}\right] = \begin{bmatrix}

a_{11} & a_{13} & a_{14} \\ a_{21} & a_{23} & a_{24} \end{bmatrix}$

is a submatrix of $\mathbf A$ formed by rows $1, 2$ and columns $1, 3, 4$.

This submatrix can also be denoted by $\mathbf A \left({3; 2}\right)$ which means that it is formed by deleting row $3$ and column $2$.