Inverse matrix

An $ n\times n$ matrix (square matrix) of the form

$\displaystyle \begin{bmatrix}
1 & 0 & \cdots & 0 \\
0 & 1 & \cdots & 0 \\
\hdotsfor{4} \\
0 & 0 & \cdots & 1
\end{bmatrix}$

is called the $ n\times n$ identity matrix, and denoted by $ I_n$.

Let $ A$ be an $ n\times n$ matrix. If there exists an $ n\times n$ matrix $ C$ satisfying $ A C = I_n$ and $ C A = I_n$, then $ A$ is said to be invertible, and $ C$ is called the inverse of $ A$, denoted by $ A^{-1}$. If $ A$ is not invertible, we call $ A$ a singular matrix.

In Matlab/Octave the function eye(n) generates the $ n\times n$ identity matrix. For example,

> eye(5)
creates the $ 5\times 5$ identity matrix.

EXAMPLE 1 Find $ 3\times 3$ and $ 5\times 5$ identity matrix.



Subsections

Department of Mathematics
Last modified: 2005-10-21