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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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