np.linalg.norm() for vector norms in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does np.linalg.norm() compute when applied to a vector?

np.linalg.norm() calculates the length or size of a vector, also called the vector's norm.

beginner

How do you calculate the Euclidean norm (length) of a vector v using np.linalg.norm()?

Use np.linalg.norm(v). This gives the straight-line distance from the origin to the point represented by v.

intermediate

What parameter do you use in np.linalg.norm() to calculate the Manhattan norm (sum of absolute values)?

Set ord=1 in np.linalg.norm() to get the Manhattan norm, which sums the absolute values of vector elements.

intermediate

What does np.linalg.norm(v, ord=np.inf) compute?

It computes the maximum absolute value among the elements of vector v, called the infinity norm.

advanced

If you want to calculate the squared Euclidean norm of a vector v efficiently, what is a good approach?

Calculate np.dot(v, v) instead of np.linalg.norm(v)**2 to avoid the square root and save computation.

What is the default norm calculated by np.linalg.norm() when applied to a vector?

A Euclidean norm (L2 norm)

B Manhattan norm (L1 norm)

C Infinity norm

D Squared Euclidean norm

The default is the Euclidean norm, which is the square root of the sum of squares of the vector elements.

Which ord value in np.linalg.norm() gives the Manhattan norm?

A np.inf

B 0

C 2

D 1

Setting ord=1 calculates the Manhattan norm, the sum of absolute values.

What does np.linalg.norm(v, ord=np.inf) return?

A Sum of vector elements

B Maximum absolute value

C Minimum absolute value

D Euclidean norm

It returns the maximum absolute value among the vector elements, known as the infinity norm.

How can you compute the squared Euclidean norm of a vector v efficiently?

A np.linalg.norm(v)**2

B np.sum(v)

C np.dot(v, v)

D np.linalg.norm(v, ord=2)

Using np.dot(v, v) avoids the square root and is faster for squared norm.

What will np.linalg.norm([3, 4]) return?

A 5

B 25

C 12

D 7

The Euclidean norm is sqrt(3² + 4²) = 5.

Explain how to use np.linalg.norm() to calculate different types of vector norms and give examples.

Think about the 'ord' parameter and what each norm means.

Describe why and how you might compute the squared Euclidean norm of a vector without using np.linalg.norm().

Consider the math behind Euclidean norm and dot product.