在数学中,数量积(dot product; scalar product,也称为点积)是接受在实数R上的两个向量并返回一个实数值标量的二元运算。它是欧几里得空间的标准内积。
两个向量a = [a1, a2,…, an]和b = [b1, b2,…, bn]的点积定义为:
a·b=a1b1+a2b2+……+anbn。
使用矩阵乘法并把(纵列)向量当作n×1 矩阵,点积还可以写为:
a·b=a^T*b,这里的a^T指示矩阵a的转置。
追答![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/b219ebc4b74543a95d16d8da16178a82b9011492?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
内积
长度自然为0
不不不,内积自然为0
a的长度
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/314e251f95cad1c83d39de31773e6709c93d5121?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
同理得b的长度
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/b58f8c5494eef01f4f1635d3e8fe9925bc317da1?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
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