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=[apk]m*n
where a11,a12,a13,a14 etc are elements of matrix and element apk are pthrow and kth 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 apk=0 for all p ≠ k and apk=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. apk=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. apk=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. apk=0 for all p <k