Matrix Nullity Calculator

Enter the total number of columns and the rank into the calculator to determine the nullity of a matrix. This calculator can also evaluate any of the variables given the others are known.

• Matrix Transpose Calculator
• Matrices Rank Calculator
• Matrix Determinant Calculator (2×2)

Matrix Nullity Formula

The following formula is used to calculate the nullity of a matrix.

Nullity(M) = n - Rank(M)

Variables:

• Nullity(M) is the nullity of the matrix M
• n is the total number of columns in the matrix M
• Rank(M) is the rank of the matrix M

To calculate the nullity of a matrix, subtract the rank of the matrix from the total number of columns in the matrix. The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. The nullity of a matrix is the dimension of the null space of the matrix, which is the set of all vectors that when multiplied by the matrix, result in the zero vector.

What is a Matrix Nullity?

Matrix nullity refers to the dimension of the null space of a matrix, which is the set of all vectors that, when multiplied by the matrix, result in a zero vector. In other words, it is the number of linearly independent solutions to the homogeneous equation Ax = 0. The nullity of a matrix can provide important information about the matrix’s properties and its rank.