In linear algebra, the rank of a matrix is defined as the maximum number of linearly independent rows or columns of the matrix. Computing the rank of a matrix is an important operation in many areas of mathematics and engineering. NumPy is a popular Python library for scientific computing, and it provides convenient functionalities to compute the matrix rank, some of which are mentioned below:
1. Using "np.linalg.matrix_rank()" function:
The simplest method to compute the rank of a matrix using a NumPy array is to use the np.linalg.matrix_rank() function.
- Import the NumPy library.
- Create a matrix using NumPy.
- Use the
matrix_rank()function from the linear algebra module of NumPy to calculate the rank of the matrix. - The rank of a matrix is the number of linearly independent rows or columns in the matrix.
- Print the rank of the matrix.
2. Using "np.linalg.qr()" function:
The QR decomposition is another method to compute the rank of a matrix using a NumPy array.
- Import the NumPy library
- Create a matrix using NumPy
- Compute the QR decomposition of the matrix using the
qr()function from the linear algebra module of NumPy - The QR decomposition decomposes the matrix into an orthogonal matrix “Q” and an upper triangular matrix “R”
- Calculate the rank of the matrix by counting the number of diagonal elements in the “R” matrix that are larger than a small value “(1e-10)” in absolute value
- Print the rank of the matrix
3. Using "np.linalg.eig()" function:
The eigenvalue decomposition is also a method to compute the rank of a matrix using a NumPy array.
- Import the NumPy library
- Create a matrix using NumPy
- Calculate the eigenvalues and eigenvectors of the matrix using the
eig()function from the linear algebra module of NumPy - Store the eigenvalues in the
eigenvaluesarray - Store the corresponding eigenvectors in the
eigenvectorsmatrix - Calculate the rank of the matrix by counting the number of eigenvalues that are larger than a small value “(1e-10)” in absolute value
- Print the rank of the matrix.