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Types Of Matrices

Types of Matrices Online Tutoring / Homework Help
  • Row Matrix: A matrix which has only one row and any number of columns is known as a row matrix. Generally a row matrix is denoted by A = [aij]1n of order 1 n.

    Example: [2 4 6 8] has one row and 4 columns hence this is a row matrix of order 1 4.

  • Column Matrix: A matrix which has only one column and any number of rows is named as a column matrix. Generally a column matrix is denoted by A = [aij]m1 of order m 1.

    Example: has 4 rows and 1 column hence this is a column matrix of order 4 1.

  • Square Matrix: A matrix in which the number of rows and number of columns are equal is called a square matrix. Generally a square matrix is denoted by A = [aij]mm of order m.


    Examples: [2] is a square matrix of order 1 1, is a square matrix of order

    2 2 and is a square matrix of order 3 3.

  • Diagonal Matrix: A square matrix is known as a diagonal matrix if all the elements other than the diagonal elements are zero. Hence the square matrix [aij] is a diagonal matrix if aij = 0 for i ≠ j.

    Example: is a diagonal matrix.

  • Identity Matrix: A square matrix is named as an identity matrix if all the elements of the main diagonal are 1. Hence the square matrix [aij] is an identity matrix if

    aij =

    Identity matrix is denoted by I.

    Examples: [3], , etc. are identity matrices of order 1, 2 and 3 respectively.

  • Zero Matrix (or Null Matrix): A matrix is known as a zero or null matrix if all of its elements are zero.

    Examples: [0], , [0, 0], etc. are all zero matrices.

  • Scalar Matrix: A diagonal matrix is called a scalar matrix if all the elements of the main diagonal are equal to the same non-zero constant, say c. Hence the square matrix [aij] is a scalar matrix if

    aij =

    Examples: [4], , etc. are scalar matrices of order 1 1, 2 2 and 3 3 respectively.



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