理解一维向量上的 np.matmul

Question

a = [1, 2, 3]
b = [10, 10, 10]

np.matmul(a, b) 结果为 60。

numpy如何将(3,)和(3,)维相乘并且returns点积不是外积(3 * 3)或抛出错误"dimension not matching"?

Answer 1

这直接来自 numpy.matmul() 的文档：

• If the first argument is 1-D, it is promoted to a matrix by prepending a 1 to its dimensions. After matrix multiplication the prepended 1 is removed.
• If the second argument is 1-D, it is promoted to a matrix by appending a 1 to its dimensions. After matrix multiplication the appended 1 is removed.

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因此，在矩阵乘法期间，输入 a 和 b 的形状分别转换为 (1, 3) 和 (3,1)。

根据矩阵乘法的规则，我们知道：

1 x 3 3 x 1
| |
-------- ===> 求和了。

因此，我们得到的结果是 标量。