Linear Algebra with Applications, 10th Edition

Submatrices

To refer to a submatrix of the matrix A entered earlier, use the: to specify the rows and columns. For example, the submatrix consisting of the entries in the second two rows of columns 2 through 4 is given by $A(2:3,2:4)$. Thus, the statement

$$C=A(2:3,2:4)$$

generates

$$\begin{array}{c}\hfill C=\\ \hfill 6& \hfill 7& \hfill 8\\ \hfill 10& \hfill 11& \hfill 12\end{array}$$

If the colon is used by itself for one of the arguments, either all the rows or all the columns of the matrix will be included. For example, $A(:,2:3)$ represents the submatrix of A consisting of all the elements in the second and third columns, and $A(4,:)$ denotes the fourth row vector of A. We can generate a submatrix using non-adjacent rows or columns by using vector arguments to specify which rows and columns are to be included. For example, to generate ...