matlab - 运算符 "dot"(.) 是什么意思？

Question

给定代码:

 A = [1 2 3; 3 2 1]
 B = A.^2

输出:

B =

     1     4     9
     9     4     1

但如果我这样做:B = A^2

输出是:

Error using  ^ 
Inputs must be a scalar and a square matrix.
To compute elementwise POWER, use POWER (.^) instead.

运算符 . 究竟做了什么？

Answer 1

点本身不是运算符，.^ 是。

.^ 是逐点 ¹(即逐元素)幂，因为 .* 是 pointwise product .

.^ Array power. A.^B is the matrix with elements A(i,j) to the B(i,j) power. The sizes of A and B must be the same or be compatible.

比照

• “数组与矩阵运算”:https://mathworks.com/help/matlab/matlab_prog/array-vs-matrix-operations.html
• “逐点”:http://en.wikipedia.org/wiki/Pointwise
• “基于元素的操作”:http://www.glue.umd.edu/afs/glue.umd.edu/system/info/olh/Numerical/Matlab_Matrix_Manipulation_Software/Matrix_Vector_Operations/elementwise

¹) 因此点。