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.