Sum of Products Calculator
About Sum of Products
The sum of products is calculated by multiplying corresponding elements from two sets and adding the results.
Formula:
Σ(aᵢ × bᵢ) = a₁b₁ + a₂b₂ + ... + aₙbₙ
Example:
Set A: [1, 2, 3]
Set B: [4, 5, 6]
Sum = (1×4) + (2×5) + (3×6) = 4 + 10 + 18 = 32
Σ(aᵢ × bᵢ) = a₁b₁ + a₂b₂ + ... + aₙbₙ
Example:
Set A: [1, 2, 3]
Set B: [4, 5, 6]
Sum = (1×4) + (2×5) + (3×6) = 4 + 10 + 18 = 32
Properties:
- The sum of products is commutative (Σ(aᵢ × bᵢ) = Σ(bᵢ × aᵢ))
- It's distributive over addition
- Used in dot product calculations
- Important in linear algebra and statistics
Applications:
- Vector dot products
- Statistical calculations
- Signal processing
- Machine learning
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