np.dot() for dot product in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does np.dot() function do in numpy?

np.dot() calculates the dot product of two arrays. For 1D arrays, it returns the sum of products of corresponding elements. For 2D arrays, it performs matrix multiplication.

beginner

How does np.dot() behave differently for 1D and 2D arrays?

For 1D arrays, np.dot() returns the scalar dot product (sum of element-wise products). For 2D arrays, it returns the matrix product (like multiplying two matrices).

beginner

Example: What is the result of np.dot([1, 2, 3], [4, 5, 6])?

The result is 1*4 + 2*5 + 3*6 = 32. So, np.dot([1, 2, 3], [4, 5, 6]) returns 32.

intermediate

What shape requirements must two arrays meet to use np.dot() for matrix multiplication?

For 2D arrays, the number of columns in the first array must equal the number of rows in the second array to perform matrix multiplication with np.dot().

beginner

How can np.dot() be used in real life?

It can calculate projections, combine data with weights, or multiply matrices in graphics, physics, or machine learning tasks.

What does np.dot() return when given two 1D arrays?

A A scalar representing the sum of element-wise products

B A matrix product

C A concatenated array

D An error

For 1D arrays, np.dot() returns the scalar dot product, which is the sum of the products of corresponding elements.

If A is shape (3, 2) and B is shape (2, 4), what will np.dot(A, B) produce?

A An error due to shape mismatch

B An array of shape (2, 2)

C An array of shape (3, 2)

D An array of shape (3, 4)

The dot product of (3, 2) and (2, 4) arrays results in a (3, 4) array.

What happens if you try np.dot() on two arrays where the inner dimensions don't match?

A It concatenates the arrays

B It raises a ValueError

C It returns zero

D It returns None

If the inner dimensions don't match for matrix multiplication, np.dot() raises a ValueError.

Which of these is a correct use of np.dot()?

A Calculating the angle between two vectors

B Adding two arrays element-wise

C Finding the maximum value in an array

D Sorting an array

The dot product is used to calculate the angle between vectors among other things.

What is the output of np.dot([[1, 2], [3, 4]], [[5, 6], [7, 8]])?

A [[5 6] [7 8]]

B [[6 8] [10 12]]

C [[19 22] [43 50]]

D [[12 16] [20 24]]

The matrix product is [[1*5+2*7, 1*6+2*8], [3*5+4*7, 3*6+4*8]] = [[19, 22], [43, 50]].

Explain how np.dot() works differently for 1D and 2D arrays.

Think about vectors vs matrices.

Describe a real-life example where you might use np.dot().

Consider tasks involving vectors or matrices.