This is more confusing then it helps. Why mix concepts of Linear Algebra/Physics with basic Arithmetics for no good reason? The multiplication, that is just r

This is more confusing then it helps. Why mix concepts of Linear Algebra/Physics with basic Arithmetics for no good reason? The multiplication, that is just repeated addition, is very possible in dimensional analysis and is called scalar multiplication: The outright worst part is this weird complication: 2 baskets × 3 apples per basket = 6 apples of 2 x 3 apples = 6 apples. Just why? This is just a scalar operation. Staying in strictly mathematical concepts, the operation described in OP are closer to the cross product of orthogonal vectors, then multiplication in my opinion. [4 0 0] × [0 3 0] = [0 0 12] https://en.wikipedia.org/wiki/Scalar_multiplication https://en.wikipedia.org/wiki/Scalar_multiplication https://en.wikipedia.org/wiki/Cross_product#Geometric_meaning https://en.wikipedia.org/wiki/Cross_product#Geometric_meanin...