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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.

m by n matrix in algebra

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. example of square matrix

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.
row matrix example

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


example of column matrix

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

example of diagonal matrix

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

example of unit matrix

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

example of null matrix

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

example of upper triangular matrix

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

example of lower triangular matrix
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