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Dot Product From Scratcheasy

Dot Product From Scratch

easy Math for ML 10–15 min

NumPy allowed · plain Python earns 10 bonus points

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Interactive Vector Lab

Vector Dot Product

Pairwise coordinate multiplication and accumulation: a · b = Σ (a_i × b_i)
Editable Inputs (change values live)Step 0 of 3
a =
b =
Click Step → or Play to walk through pairwise multiplication and accumulation.
dot = (1 × 4) + (2 × 5) + (3 × 6)= …
Live Result32

Implement the dot product from scratch, understand exactly what every multiplication and addition is doing, then connect the operation to the computations inside modern AI systems.

Task

Implement dot_product(a, b) using plain Python or NumPy. Libraries are allowed; a plain-Python solution earns 10 bonus points.

Function Signature

dot_product(a: list[float], b: list[float]) -> float

Examples

Example 1: Basic Case
Input: a = [1, 2, 3] b = [4, 5, 6]
Output: 32
Explanation: 1*4 + 2*5 + 3*6 = 32
Example 2: Zero Vector
Input: a = [0, 0] b = [5, 5]
Output: 0
Explanation: Zero vector produces 0
Example 3: Negative Values
Input: a = [-1, 2] b = [3, -4]
Output: -11
Explanation: -1*3 + 2*-4 = -11
Example 4: Single Element
Input: a = [2] b = [3]
Output: 6
Explanation: 2*3 = 6

Constraints

  • Libraries (NumPy) are allowed and accepted normally.
  • A plain-Python solution (no NumPy) earns 10 bonus points.
  • Must raise ValueError if len(a) != len(b).
  • Must handle floating-point values and negative numbers correctly.
Python3Saved ✓
def dot_product(a: list[float], b: list[float]) -> float:
"""Return the dot product of two equal-length lists of numbers.
Raise ValueError if len(a) != len(b)."""
# Your implementation here
pass

Case 1: Basic Case
Input: a = [1, 2, 3] b = [4, 5, 6]
Expected: 32
Case 2: Zero Vector
Input: a = [0, 0] b = [5, 5]
Expected: 0
Case 3: Negative Values
Input: a = [-1, 2] b = [3, -4]
Expected: -11
Case 4: Single Element
Input: a = [2] b = [3]
Expected: 6