# Matrices

Matrices is a set of real or imaginary number that arranged in the form of a rectangular array(rectangualr box) . array like A[m][n] where m represent row and n represent column is known as m*n or m by n matrix.

We can also represent m by n matrix as A=[a_{pk}]_{m*n}

where a_{11},a_{12},a_{13},a_{14} etc are elements of matrix and element a_{pk} are p^{th}row and k^{th} column element of metrix.

## Type of Matrices in Algebra

- Square matrix
- Row matrix
- Column matrix
- Scalar matrix
- Diagonal matrix
- Unit matrix
- Null matrix
- Upper triangular matrix
- Lower triangular matrix

**Square matrix :**A square matrix is a matrix which number of row is equal to the number of columns.

**Row matrix :**A row matrix is a matrix that have only one row.it also known as row vector.
Example of row matrix A=[3 5 -3 -1] order of row matrix is represented by 1*n only one row with multiple column.

**Column matrix :**A column matrix is a matrix that have only one column.

**Scalar matrix :** A square matrix is called a scalar matrix if a_{pk}=0 for all p ≠ k and a_{pk}=C for all p , C≠0

means leading diagonal elements are equal(not zero) and other element are zero

**Diagonal matrix :** If all the elements, except those in the leading diagonal of square matrix are zero then matrix known as diagonal matrix.
a_{pk}=0 for all p≠k

**Unit matrix :**Square matrix is known as unit matrix if leading diagonal elements of square matrix is 1 and other element is equal to zero

**Null matrix :** Matrix is called null matrix or **zero matrix** if all elements of metrix are zero.

**Upper triangular matrix :**A square matrix is called a Upper triangular matrix if all elements below the leading diagonal are zero. a_{pk}=0 for all p >k

**Lower triangular matrix :** A square matrix is called a Lower triangular matrix if all elements above the leading diagonal are zero. a_{pk}=0 for all p <k