# Definition of square matrix

Put content here.**Definition:** A **square matrix** is a matrix with the same number of rows and columns. An $n \times n$ matrix is called a square matrix of **order $n$**.
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$$A = \begin{pmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{n1} & a_{n2} & \cdots & a_{nn} \end{pmatrix}$$
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**Example:**
$$A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$$
is a $2 \times 2$ square matrix.
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Square matrices are particularly important because they:
- Have a well-defined **determinant**
- May have an **inverse** (if nonsingular)
- Represent **linear operators** from a vector space to itself
- Have **eigenvalues** and **eigenvectors**

# Parents

* Basic terminology and notation