R中的矩阵和向量乘法运算

我觉得R中的矩阵运算非常令人困惑:我们正在混合行向量和列向量.

I feel matrix operations in R is very confusing: we are mixing row and column vectors.

• 在这里，我们将x1定义为一个向量，(我假设R默认向量是列向量吗?但是它没有显示它是按这种方式排列的.)

• Here we define x1 as a vector, (I assume R default vector is a column vector? but it does not show it is arranged in that way.)

然后我们定义x2是x1的转置，这对我来说也很奇怪.

Then we define x2 is a transpose of x1, which the display also seems strange for me.

最后，如果我们将x3定义为矩阵，则显示效果会更好.

Finally, if we define x3 as a matrix the display seems better.

现在，我的问题是，x1和x2是完全不同的东西(一个是另一个的转置)，但是我们在这里得到的结果是相同的.

Now, my question is that, x1 and x2 are completely different things (one is transpose of another), but we have the same results here.

有什么解释吗?也许我不应该将向量和矩阵运算混合在一起吗?

Any explanations? may be I should not mix vector and matrix operations together?

x1 = c(1:3)
x2 = t(x1)
x3 = matrix(c(1:3), ncol = 1)

x1
[1] 1 2 3

x2
     [,1] [,2] [,3]
[1,]    1    2    3

x3
     [,1]
[1,]    1
[2,]    2
[3,]    3

x3 %*% x1
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    2    4    6
[3,]    3    6    9

x3 %*% x2
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    2    4    6
[3,]    3    6    9