Define scalar product. Write any two characteristics
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The dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers and returns a single number. Properties:
Commutative: .
Distributive over vector addition:
Bilinear:
Scalar multiplication:
Not associative because the dot product between a scalar (a ⋅ b) and a vector (c) is not defined, which means that the expressions involved in the associative property, (a ⋅ b) ⋅ c or a ⋅ (b ⋅ c) are both ill-defined.
Orthogonal.
Commutative: .
Distributive over vector addition:
Bilinear:
Scalar multiplication:
Not associative because the dot product between a scalar (a ⋅ b) and a vector (c) is not defined, which means that the expressions involved in the associative property, (a ⋅ b) ⋅ c or a ⋅ (b ⋅ c) are both ill-defined.
Orthogonal.
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