 # Matrices and Their Types

## •    A matrix is an ordered rectangular array of numbers or functions arranged in rows and columns. A matrix having m rows and n columns is called a matrix of order m x n. In general, an m × n matrix is represented as below:•    Two matrices are comparable matrices iff each one of them contains as many rows and columns as the other.•    Two matrices are said to be equal if they are of the same order and each element of matrix A is equal to the corresponding element of matrix B.•    A matrix is said to be a column matrix if it has only one column.•    A matrix is said to be a row matrix if it has only one row.•    A matrix in which the number of rows is equal to the number of columns, is said to be a square matrix.•    A square matrix is said to be a diagonal matrix if all its non diagonal elements are zero.•    A diagonal matrix is said to be a scalar matrix if all its diagonal elements are equal.•    The diagonal matrix in which each diagonal element is equal to unity is called an identity matrix. •    A matrix is said to be zero matrix or null matrix if all its elements are zero.•    A square matrix is said to be an upper triangular matrix iff all the elements below the principal diagonal are zero.•    A square matrix is said to be a lower triangular matrix iff all the elements above the principal diagonal are zero.•    A triangular matrix is said to be strictly triangular matrix if and only if all the elements of the principal diagonal are zero.Keywords: Matrix, Types of Matrices, Identity Matrix, Equal Matrices, Scalar Matrix, Diagonal Matrix, Order of a Matrix, Comparable Matrices, Column Matrix, Row Matrix, Square Matrix, Zero Matrix

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• Q1

A matrix in which all non diagonal elements are zero is known as

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diagonal matrix.

##### Explanation:
A square matrix B = [bij]m×n is said to be a diagonal matrix, if all its non diagonal elements are zero, that is a matrix B = [bij]m×n is said to be a diagonal matrix, if bij = 0, when i ¹ j.
• Q2

A matrix, in which the number of rows is equal to the number of columns, is known as

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square matrix.

##### Explanation:

A matrix is said to be a square matrix, if it has the number of rows equal to the number of columns.

An m n matrix is said to be a square matrix, if m = n and is known as a square matrix of order ‘n’.

• Q3

A matrix having only one row is known as

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row matrix.

##### Explanation:

A matrix is said to be a row matrix, if it has only one row.

In general, A = [aij]n is a column matrix of order 1 n.

• Q4

A matrix having only one column is known as

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column matrix.

##### Explanation:

A matrix is said to be a column matrix, if it has only one column.

In genral, A = [aij]m×1 is a column matrix of order m 1.

m n.
A matrix having m rows and n columns is called a matrix of order m n or simply m × n matrix (read as an m by n matrix).