np.linalg.norm() for vector norms in NumPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the Euclidean norm of vector v.

NumPy

import numpy as np
v = np.array([3, 4])
norm = np.linalg.norm([1])
print(norm)

Drag options to blanks, or click blank then click option'

Anp.linalg

B[3, 4]

Cnp.array([3, 4])

Dv

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the numpy module instead of the vector.

Passing a list instead of the numpy array variable.

The function np.linalg.norm() calculates the length (norm) of the vector passed to it. Here, v is the vector.

2fill in blank

medium

Complete the code to calculate the 1-norm (sum of absolute values) of vector x.

NumPy

import numpy as np
x = np.array([-1, 2, -3])
norm_1 = np.linalg.norm(x, ord=[1])
print(norm_1)

Drag options to blanks, or click blank then click option'

A2

Bnp.inf

C1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using ord=2 which is the default Euclidean norm.

Using ord=0 which is not a valid norm for vectors.

The ord=1 argument tells np.linalg.norm() to compute the 1-norm, which is the sum of absolute values of the vector elements.

3fill in blank

hard

Fix the error in the code to correctly compute the infinity norm (max absolute value) of vector y.

NumPy

import numpy as np
y = np.array([1, -5, 3])
norm_inf = np.linalg.norm(y, ord=[1])
print(norm_inf)

Drag options to blanks, or click blank then click option'

Ainf

Bnp.inf

Cfloat('inf')

Dinfinity

Attempts:

3 left

💡 Hint

Common Mistakes

Using string 'inf' instead of np.inf.

Using float('inf') which is not accepted here.

The correct way to specify the infinity norm in np.linalg.norm() is ord=np.inf. Other options cause errors or are invalid.

4fill in blank

hard

Fill both blanks to create a dictionary of vector norms for each vector in the list.

NumPy

import numpy as np
vectors = [np.array([1, 2]), np.array([3, 4])]
norms = {i: np.linalg.norm(vectors[[1]], ord=[2]) for i in range(len(vectors))}
print(norms)

Drag options to blanks, or click blank then click option'

Ai

B0

C1

D2

Attempts:

3 left

💡 Hint

Common Mistakes

Using a fixed index instead of the loop variable.

Using an invalid norm order.

The loop variable i is used to index each vector in the list. Using ord=1 computes the 1-norm for each vector.

5fill in blank

hard

Fill all three blanks to create a dictionary of Euclidean norms for vectors longer than 2 elements.

NumPy

import numpy as np
vectors = [np.array([1, 2]), np.array([3, 4, 5]), np.array([6, 7, 8, 9])]
norms = {i: np.linalg.norm(vectors[[1]], ord=[2]) for i in range(len(vectors)) if len(vectors[[3]]) > 2}
print(norms)

Drag options to blanks, or click blank then click option'

Ai

B2

C1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using different indices for vector access and length check.

Using wrong norm order.

The loop variable i (option A) is used to index vectors. The Euclidean norm is ord=2. The length check uses the same index i.

Practice

1. What does np.linalg.norm() calculate by default when given a vector?

easy

A. The maximum element in the vector

B. The sum of all vector elements

C. The Euclidean length (distance) of the vector

D. The product of all vector elements

Solution

1. Step 1: Understand the default behavior of np.linalg.norm()

   By default, np.linalg.norm() calculates the Euclidean norm, which is the straight-line distance from the origin to the point represented by the vector.

2. Step 2: Compare with other options

   The sum, max, and product are different operations and not what np.linalg.norm() returns by default.

3. Final Answer:

   The Euclidean length (distance) of the vector -> Option C

4. Quick Check:

   Default norm = Euclidean length [OK]

Hint: Default norm is Euclidean distance, not sum or max [OK]

Common Mistakes:

• Confusing norm with sum of elements
• Thinking norm returns max element
• Assuming norm multiplies elements

2. Which of the following is the correct syntax to compute the 1-norm (sum of absolute values) of a vector v using np.linalg.norm()?

easy

A. np.linalg.norm(v, order=1)

B. np.linalg.norm(v, ord=1)

C. np.linalg.norm(v, norm=1)

D. np.linalg.norm(v, p=1)

Solution

1. Step 1: Recall the parameter name for norm order

   The parameter to specify the norm order in np.linalg.norm() is ord, not order, norm, or p.

2. Step 2: Check the correct syntax

   Using ord=1 correctly computes the 1-norm, which sums the absolute values of vector elements.

3. Final Answer:

   np.linalg.norm(v, ord=1) -> Option B

4. Quick Check:

   Use ord=1 for 1-norm [OK]

Hint: Use ord=1 to specify 1-norm in np.linalg.norm() [OK]

Common Mistakes:

• Using 'order' instead of 'ord'
• Using 'norm' or 'p' as parameter names
• Omitting the ord parameter for 1-norm

3. What is the output of the following code?

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

medium

A. 5.0

B. 7

C. 12

D. 1

Solution

1. Step 1: Calculate the Euclidean norm of vector [3, 4]

   The Euclidean norm is sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5.0.

2. Step 2: Confirm the printed output

   The code prints the norm value, which is 5.0.

3. Final Answer:

   5.0 -> Option A

4. Quick Check:

   Euclidean norm of [3,4] = 5.0 [OK]

Hint: Euclidean norm of (3,4) is 5 by Pythagoras [OK]

Common Mistakes:

• Adding elements instead of squaring and summing
• Forgetting to take square root
• Confusing norm with sum or max

4. The following code throws an error. What is the mistake?

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

medium

A. The parameter name should be 'ord' not 'order'

B. The vector contains negative values which cause error

C. np.linalg.norm() does not accept a second argument

D. The vector must be a list, not a numpy array

Solution

1. Step 1: Identify the parameter name error

   The parameter to specify norm order is ord, not order. Using order causes a TypeError.

2. Step 2: Confirm other options are incorrect

   Negative values are allowed, np.linalg.norm accepts second argument ord, and numpy arrays are valid inputs.

3. Final Answer:

   The parameter name should be 'ord' not 'order' -> Option A

4. Quick Check:

   Use ord=2, not order=2 [OK]

Hint: Use ord= for norm order, not order= [OK]

Common Mistakes:

• Using 'order' instead of 'ord'
• Thinking negative values cause error
• Believing np.linalg.norm takes only one argument

5. You have a dataset of 2D points stored as rows in a numpy array points. You want to normalize each point to have length 1 (unit vector). Which code correctly does this using np.linalg.norm()?

hard

A. normalized = points / np.linalg.norm(points, ord=1, axis=1)

B. normalized = points / np.linalg.norm(points, axis=0)

C. normalized = points / np.linalg.norm(points)

D. normalized = points / np.linalg.norm(points, axis=1, keepdims=True)

Solution

1. Step 1: Calculate norms along rows with correct shape

   Using np.linalg.norm(points, axis=1, keepdims=True) computes the Euclidean norm for each row and keeps the result as a column vector, allowing correct broadcasting for division.

2. Step 2: Normalize each point by dividing by its norm

   Dividing points by the norms with matching shape normalizes each row vector to length 1.

3. Final Answer:

   normalized = points / np.linalg.norm(points, axis=1, keepdims=True) -> Option D

4. Quick Check:

   Use keepdims=True for correct broadcasting [OK]

Hint: Use keepdims=True to keep norm shape for division [OK]

Common Mistakes:

• Using axis=0 instead of axis=1 for row-wise normalization
• Using norm of whole array instead of per row
• Using ord=1 instead of default Euclidean norm