Properties of a Singular Matrix
The following are the properties of the Singular Matrix:
- Every singular matrix must be a square matrix, i.e., a matrix that has an equal number of rows and columns.
- Determinant of a singular matrix is equal to zero.
- As the determinant of a singular matrix is zero, its inverse is not defined.
- A zero matrix of any order matrix is a singular matrix, as its determinant is zero.
- In a singular matrix, some rows and columns are linearly dependent.
- Rank of a singular matrix will be less than the order of the matrix, i.e., Rank (A) < Order of A.
- A matrix that has any two rows or any two columns identical is singular, as the determinant of such a matrix is zero.
- When a row or column’s elements in a matrix are all zeros, then the matrix is singular, as its determinant is zero.
- When one row (or column) of a matrix is a scalar multiple of another row (or column), then the matrix is singular as its determinant is zero.
Singular Matrix
Singular Matrix: A singular matrix is a square matrix of determinant “0.” i.e., a square matrix A is singular if and only if det A = 0. Inverse of a matrix A is found using the formula A-1 = (adj A) / (det A). Thus, a matrix is called a square matrix if its determinant is zero.
Now let us discuss about singular matrix, its properties, and others in detail.
Table of Content
- What is a Singular Matrix?
- Singular Matrix Definition
- Properties of a Singular Matrix
- Differences Between Singular and Non-Singular Matrix
- Identifying a Singular Matrix
- Formula for Determinant of “2 × 2” Matrix
- Formula for Determinant of “3 × 3” Matrix
- Articles related to Singular Matrix:
- Solved Examples on Singular Matrix