Return the negative infinity Norm of the matrix in Linear Algebra in Python

To return the negative infinity norm of a matrix in Linear Algebra, use the LA.norm() method with -np.inf as the order parameter. The negative infinity norm returns the minimum row sum of absolute values in the matrix.

Syntax

numpy.linalg.norm(x, ord=-np.inf, axis=None, keepdims=False)

Parameters

The key parameters for calculating negative infinity norm ?

• x − Input array (1-D or 2-D)
• ord − Order of norm. Use -np.inf for negative infinity norm
• axis − Axis along which to compute the norm (default: None)
• keepdims − Whether to keep dimensions in result (default: False)

How Negative Infinity Norm Works

The negative infinity norm calculates the minimum of the sum of absolute values across each row of the matrix. For a matrix with rows containing absolute sums [9, 2, 9], the negative infinity norm would be 2 (the minimum value).

Example

import numpy as np
from numpy import linalg as LA

# Create a matrix
arr = np.array([[-4, -3, -2],
                [-1,  0,  1],
                [ 2,  3,  4]])

# Display the array
print("Our Array:")
print(arr)

# Check array properties
print("\nDimensions:", arr.ndim)
print("Datatype:", arr.dtype)
print("Shape:", arr.shape)

# Calculate negative infinity norm
result = LA.norm(arr, -np.inf)
print("\nNegative Infinity Norm:", result)

# Show row sums for understanding
row_sums = np.sum(np.abs(arr), axis=1)
print("Row sums of absolute values:", row_sums)
print("Minimum row sum (negative inf norm):", np.min(row_sums))

Our Array:
[[-4 -3 -2]
 [-1  0  1]
 [ 2  3  4]]

Dimensions: 2
Datatype: int64
Shape: (3, 3)

Negative Infinity Norm: 2.0
Row sums of absolute values: [9 2 9]
Minimum row sum (negative inf norm): 2.0

Comparison with Other Norms

Conclusion

The negative infinity norm using LA.norm(matrix, -np.inf) returns the minimum row sum of absolute values. This norm is useful in optimization and numerical analysis for measuring matrix properties.