Strassen Seven-Product Multiplication
Reconstruct a matrix product from seven carefully combined multiplications.
Free theory articleReconstruct a matrix product from seven carefully combined multiplications.
Concept & interpretation
Matrix multiplication is famously cubic—multiplying two n×n matrices classically requires eight multiplications for a 2×2 block, scaling as O(n³). In 1969, Volker Strassen discovered a clever algebraic reorganization that computes the product using only seven multiplications, leading to an asymptotic complexity of O(n^log₂(7)) ≈ O(n²·⁸¹).
Tracing the Algorithm
Use the interactive module to see exactly how the elements of A and B are combined to form the 7 products, and how those products reconstruct C.
- Select the Matrix pair control to choose between General, Signed, Zero, or Identity presets.
- Adjust the Left scale to see how scaling a matrix affects the intermediate products.
- Observe how the 7 products are derived and verify the arithmetic for the reconstruction of C.
Explore the full trace in the Strassen Seven-Product Multiplication module.