vector-spaces #

Animated, step-by-step view of a vector space as an additive abelian group of vectors (showing 0, inverses, and vector addition) together with a field F whose scalars act on vectors via scalar multiplication. The final scene presents a commutative-diagram style check of a compatibility axiom (distributivity), emphasizing that scalar action respects vector addition.

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

01.Understanding why linear combinations work (core to solving linear systems)
02.Interpreting scaling and addition in graphics/physics as structure-preserving operations
03.Recognizing the role of fields F (e.g., real numbers) in defining valid scalar multiplication rules

technical notes #

Uses a 4-scene loop (4s total) with cubic easing for smooth transitions. Layout is responsive via scale = min(w,h)/240 and all geometry is snapped to a small grid for a retro blocky aesthetic. Draws vectors with arrowheads and a faint grid; shows the field-action relationship with an action arrow and a distributivity diagram.

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