# Computing a Matrix Rank using NumPy

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 `eigenvalues` array
• Store the corresponding eigenvectors in the `eigenvectors` matrix
• 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.
The choice of method depends on the size of the matrix, the performance requirements, and the programmer's preferences.