# Types Of Matrices

Related Topics: Lessons and operations on Matrices

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

What is a matrix?
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.

What are the types of 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

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. 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. 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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