Geometry and algebra of linear maps, vectors, and matrices
A vector wears two hats at once. Numerically it is just an ordered list. [3, 1] means "3 then 1," and the order matters: [3, 1] is not [1, 3]. Geometrically that same list is an arrow: start at the origin, walk 3 right and 1 up, and the tip lands at the point the vector names.
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▶ Vectors in Rⁿ