In these lessons, we will learn the different types of matrices: row matrix, column matrix, zero matrix, square matrix, diagonal matrix, unit matrix and equal matrices.

**Related Pages**

Singular Matrix

Inverse Matrix

More Lessons On Matrices

A matrix is a rectangular array of numbers. The size or dimension of a matrix is defined by the number of rows and columns it contains. Matrices is plural for matrix.

The following diagrams give some of examples of the types of matrices. Scroll down the page for more examples and explanations.

A matrix may be classified by types. It is possible for a matrix to belong to more than one type.

A **row matrix** is a matrix with only one row.

**Example:** E is a row matrix of order 1 × 1

**Example:** B is a row matrix of order 1 × 3

A **column matrix** is a matrix with only one column.

**Example:** C is a column matrix of order 1 × 1

A column matrix of order 2 ×1 is also called a **vector** matrix.

**Example:** D is a column matrix of order 2 × 1

A **zero matrix** or a **null matrix**
is a matrix that has all its elements zero.

**Example:** **O** is a zero matrix of order 2 × 3

A **square matrix** is a matrix with an equal number of rows and
columns.

**Example:** T is a square matrix of order 2 × 2

**Example:** V is a square matrix of order 3 × 3

A **diagonal matrix** is a square matrix that has all its
elements zero except for those in the diagonal from top left to bottom right; which is known
as the **leading diagonal** of the matrix.

**Example:** B is a diagonal matrix.

A **scalar matrix** is a diagonal matrix where all the diagonal
elements are equal.

**Example:**
\(\left( {\begin{array}{*{20}{c}}3&0&0\\0&3&0\\0&0&3\end{array}} \right)\)

An **upper triangular matrix** is a square matrix where all the
elements located below the diagonal are zeros.

**Example:**
\(\left( {\begin{array}{*{20}{c}}2&3&{ - 2}\\0&1&4\\0&0&5\end{array}} \right)\)

A **lower triangular matrix** is a square matrix where all the
elements located above the diagonal are zeros.
**Example:**
\(\left( {\begin{array}{*{20}{c}}3&0&0\\{ - 1}&4&0\\2&5&1\end{array}} \right)\)

A **unit matrix** is a diagonal matrix whose elements in the
diagonal are all ones.

**Example:** P is a unit matrix.

**How To Organize Data In Matrices?**

Vocabulary: matrix, element, dimension, row matrix, column matrix, square matrix, zero matrix,
equal matrices.

**Introduction To Matrices**

This video explains the vocabulary used when solving matrices. Rows, Columns, Square Matrix,
Row Matrix, Column Matrix, Zero Matrix, Equal Matrices.

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