# Types Of Matrices

• 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]1×n 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]m×1 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]m×m 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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