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What are the types of Matrices

By reading this article your following problems will be answered.

What are the types of matrices.
What are square matrices.
What are diagonal matrices.
What are identity matrices.
What are upper triangular matrices.
What are lower triangular matrices.
What are symmetric matrices.
What are shew-symmetric matrices.
What are zero matrices.
What is a row matrix or a row vector.
What is a column matrix or a column vector.
  • This article discusses about types of matrices.
  • There are few types of matrices.
    1. Square matrix
    2. Diagonal matrix
    3. Identity matrix
    4. Upper triangular matrix
    5. Lower triangular matrix
    6. Symmetric matrix
    7. Shew-symmetric matrix
    8. Zero matrix
    9. Row matrix (Row vector)
    10. Column matrix (Column vector)
  • Now let’s discuss about each matrix type in detail.

1. Square matrix

  • Square matrices have equal number of rows and columns.

E.g.: 3×3, 2×2

2. Diagonal matrix

  • A matrix to be a diagonal matrix, it need to satisfy following criteria’s.
  • I should be a square matrix.
  • All non-diagonal elements are zero.
  • At least one diagonal element is non zero.
  • The following shows two examples for diagonal matrices.

3. Identity Matrix

  • In identity matrices, all diagonal elements are equal to 1 (One).
  • Identity matrices are also diagonal matrices.
  • Identity matrices are denoted by In.
  • The following are examples for identity matrices.
Identity matrix 1×1
Identity matrix 2×2
Identity matrix 3×3

4. Upper triangular matrix

  • If all the elements below diagonal elements are zero, then that matrix is an Upper triangular matrix.
  • The following example shows an upper triangular matrix.
Upper triangular matrix

5. Lower triangular matrix

  • If all the elements above diagonal elements are zero, then that matrix is a Lower triangular matrix.
  • The following example shows an upper triangular matrix.
Lower triangular matrix

6. Symmetric matrix

  • If aij = aji for all i and j then it is considered as a Symmetric matrix.
  • That means imagine if the matrix is folded diagonally by the diagonal elements, and identical elements are getting overlapped in two opposite sides, then it is a symmetric matrix.
  • The following example shows what is a symmetric matrix.
Symmetric matrix

7. Shew-Symmetric matrix

  • If all the diagonal elements are zero and inverse of the opposite side, of the diagonal elements then it is a Shew-Symmetric matrix.
  • The following example shows a shew-symmetric matrix.
Shew-Symmetric matrix

8. Zero matrix

  • If all the elements of a matrix is equal to zero, then it is a Zero matrix.
Zero matrix

9. Row matrix (Row vector)

  • A matrix with only a single row is known as a row matrix or a row vector.

10. Column matrix (Column vector)

  • A matrix with only a single column is known as a column matrix or a column vector.

Know more about Matrices

Matrices

Introduction on Matrices

What are Transpose Matrices

How to add or subtract Matrices