Difference between revisions of "Dot product"

Revision as of 19:16, 27 August 2020

Dot product

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-The dot product of two vectors a = [a1, a2, ... , an] and b = [b1, b2, ... , bn] is defined as:
+Dot product
-<math>   \mathbf{a}\cdot \mathbf{b} = \sum_{i=1}^n a_ib_i = a_1b_1 + a_2b_2 + \cdots + a_nb_n</math>
-where Σ denotes summation notation and n is the dimension of the vector space.
-In dimension 2, the dot product of vectors [a,b] and [c,d] is ac + bd. Similarly, in a dimension 3, the dot product of vectors [a,b,c] and [d,e,f] is ad + be + cf. For example, the dot product of two three-dimensional vectors [1, 3, −5] and [4, −2, −1] is
-<math>   [1, 3, -5] \cdot [4, -2, -1] = (1 \times 4) + (3 \times -2) + (-5 \times -1) = 4 - 6 + 5 = 3</math>.
-The dot product can also be obtained via transposition and matrix multiplication as follows:
-<math>\mathbf{b}^\mathrm{T}\mathbf{a} = \mathbf{a}^\mathrm{T}\mathbf{b}</math>,
-where both vectors are interpreted as column vectors, and aT denotes the transpose of a, in other words the corresponding row vector.
 [[Category:math]]
 [[Category:Term]]