properties of scalar product
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✏The scalar product of a vector and itself is a positive real number: u → ⋅ u → ⩾ 0 .
✏The scalar product is commutative: u → ⋅ v → = v → ⋅ u → .
✏The scalar product is pseudoassociative: α ( u → ⋅ v → ) = ( α u → ) ⋅ v → = u → ⋅ ( α v → ) where is a real number.
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