Keep exploring at ► Get started for free, and hurry—the first 200 people get 20% off an annual premium subscription. 0:00 Multiplying Matrices the standard way 2:05 The Strassen Method for 2x2 Matrices 3:52 Large matrices via induction 7:25 The history and the future 10:19 In this video we explore how to multiply very large matrices as computationally efficiently as possible. Then standard algorithm from linear algebra results in n^3 multiplications to multiply nxn matrices. But can we do better? The Strassen algorithm improved this to about n^2.8, first in the 2x2 case and then we can prove via induction it works in general. This improvement has seen a range of improvements over the last 50 years inching closer - but still far away - to the theoretically limit of n^2. Further Reading: Going into the details of the laser method (what happened after the Strassen algorithm I showed): The AlphaTensor AI paper: A nice summary from Quanta: Check out my MATH MERCH line in collaboration with Beautiful Equations ► COURSE PLAYLISTS: ►DISCRETE MATH: ►LINEAR ALGEBRA: ►CALCULUS I: ► CALCULUS II: ►MULTIVARIABLE CALCULUS (Calc III): ►VECTOR CALCULUS (Calc IV) ►DIFFERENTIAL EQUATIONS: ►LAPLACE TRANSFORM: ►GAME THEORY: OTHER PLAYLISTS: ► Learning Math Series ►Cool Math Series: BECOME A MEMBER: ►Join: MATH BOOKS I LOVE (affilliate link): ► SOCIALS: ►Twitter (math based): ►Instagram (photography based):