“Dot Product”的概念、定义、习题解题方法及翻译-数学辞典

单词

Dot Product

释义

Dot Product

The dot product can be defined by

(1)

where

is the angle between the vectors. It follows immediately that

is Perpendicular to

. The dot product is also called the Inner Product and written

.By writing

			(2)
			(3)

it follows that (1) yields

So, in general,

(5)

The dot product is Commutative

(6)

Associative

(7)

and Distributive

(8)

The Derivative of a dot product of Vectors is

(9)

The dot product is invariant under rotations


			(10)

where Einstein Summation has been used.

The dot product is also defined for Tensors and by

(11)

See also Cross Product, Inner Product, Outer Product, Wedge Product

References

Arfken, G. ``Scalar or Dot Product.'' §1.3 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 13-18, 1985.

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