Properties of Rank of Matrix

Properties of rank of matrix is as follows:

• Rank of a matrix is equal to the order of the matrix if it is a non-singular matrix.
• Rank of a matrix is equal to the number of non-zero rows if it is in Echelon Form.
• Rank of matrix is equal to the order of identity matrix in it if it is in normal form.
• Rank of matrix < Order of matrix if it is singular matrix.
• Rank of matrix < minimum {m, n} if it is a rectangular matrix of order m x n.
• Rank of identity matrix is equal to the order of the identity matrix.
• Rank of a zero matrix or a null matrix is zero.

Read More,

• Types of Matrices
• Transpose of a Matrix
• Inverse of Matrix

Rank of a Matrix is defined as the dimension of the vector space formed by its columns. Rank of a Matrix is a very important concept in the field of Linear Algebra, as it helps us to know if we can find a solution to the system of equations or not. Rank of a matrix also helps us know the dimensionality of its vector space.

This article explores, the concept of the Rank of a Matrix in detail including its definition, how to calculate the rank of the matrix as well as a nullity and its relation with rank. We will also learn how to solve some problems based on the rank of a matrix. So, let’s start with the definition of the rank of the matrix first.