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 Topics: Operations on Matrices

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

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. For 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. For 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. For 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.

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

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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