Last Updated 10/21/2022

Sage Essentials
Section 7: Matrix Manipulations

Special Matrices

SageMath has convenient ways to define common special matrices such as diagonal, identity, and zero matrices.

Example 2

To define the diagonal matrix  $A=\left[\begin{array}{cccc}2& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 5& 0\\ 0& 0& 0& -1\end{array}\right]$ , we list the diagonal elements with the diagonal_matrix command.

To define an identity matrix, we use the identity_matrix command. For example, the $4\times 4$ identity matrix  $I_4=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]$ is defined by identity_matrix(4).

Alternatively, an identity matrix is a diagonal matrix. For example, $I_4$  can be defined as a $4\times 4$ diagonal matrix with 1 as the diagonal elements.

Likewise, we can define the $m\times n$ zero matrices by the zero_matrix(m,n)command.

Try this!

Define the $3\times 4$ zero matrix.