np.linalg.norm() for vector norms in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of np.linalg.norm() with default parameters

What is the output of this code snippet?

NumPy

import numpy as np
v = np.array([3, 4])
result = np.linalg.norm(v)
print(result)

A 5.0

B Error

C 25.0

D 7.0

💡 Hint

Think about the length of the vector [3,4] in 2D space.

np.linalg.norm() by default calculates the Euclidean norm (L2 norm), which is sqrt(3^2 + 4^2) = 5.0.

❓ Predict Output

intermediate

Output of np.linalg.norm() with ord=1 (Manhattan norm)

What is the output of this code snippet?

NumPy

import numpy as np
v = np.array([-1, 2, -3])
result = np.linalg.norm(v, ord=1)
print(result)

A 3.7416573867739413

B 6.0

C 14.0

D Error

💡 Hint

The ord=1 norm sums the absolute values of the vector components.

The Manhattan norm sums absolute values: |−1| + |2| + |−3| = 6.0.

❓ data_output

advanced

Shape and output of np.linalg.norm() on a 2D array with axis parameter

Given the code below, what is the output printed?

NumPy

import numpy as np
arr = np.array([[1, 2, 2], [3, 4, 0]])
result = np.linalg.norm(arr, axis=1)
print(result)

A [3. 5.]

B [3. 5. 0.]

C [3. 4.]

D Error

💡 Hint

Norm is calculated row-wise because axis=1.

For each row, Euclidean norm is sqrt(sum of squares). Row 1: sqrt(1^2+2^2+2^2)=3, Row 2: sqrt(3^2+4^2+0^2)=5.

🧠 Conceptual

advanced

Effect of ord parameter on np.linalg.norm() for vectors

Which statement correctly describes the effect of the ord parameter in np.linalg.norm() when applied to a vector?

A ord=inf computes the Euclidean norm; ord=1 computes the maximum absolute value; ord=2 computes the sum of absolute values.

B ord=1 computes the Euclidean norm; ord=2 computes the sum of absolute values; ord=inf computes the minimum absolute value.

C ord=2 computes the Euclidean norm; ord=inf computes the maximum absolute value; ord=1 computes the sum of absolute values.

D ord=2 computes the minimum absolute value; ord=1 computes the maximum absolute value; ord=inf computes the sum of absolute values.

💡 Hint

Recall common vector norms: L1, L2, and max norm.

ord=2 is Euclidean norm, ord=1 is sum of absolute values, ord=inf is max absolute value.

🔧 Debug

expert

Identify the error in np.linalg.norm() usage on a matrix with ord='fro'

What error will this code raise and why?

NumPy

import numpy as np
m = np.array([[1, 2], [3, 4]])
result = np.linalg.norm(m, ord='fro', axis=1)
print(result)

A No error; output is [2.23606798 5.0]

B TypeError: ord='fro' is not supported for 2D arrays

C IndexError: axis out of range

D ValueError: 'axis' must be None when ord='fro'

💡 Hint

Check the rules for using ord='fro' with axis parameter.

Frobenius norm requires axis=None; specifying axis with ord='fro' causes ValueError.