Matlab数组乘法

* 是向量或矩阵乘法 .* 是元素乘法

a = [ 1; 2]; % column vector
b = [ 3 4]; % row vector

a*b

ans =

     3     4
     6     8

虽然

a.*b.' % .' means tranpose

ans =

     3
     8

* 是矩阵乘法,而 .* 是元素乘法。

为了使用第一个运算符,操作数在大小方面应遵守矩阵乘法规则。

对于第二个运算符,向量长度(垂直或水平方向可能不同)或矩阵大小应相等,以便进行元素乘法

* 是矩阵乘法,而 .* 是元素数组乘法

我创建了这个简短的脚本,以帮助澄清关于这两种乘法形式的挥之不去的问题。。。

%% Difference between * and .* in MatLab

% * is matrix multiplication following rules of linear algebra
% See MATLAB function mtimes() for help

% .* is Element-wise multiplication follow rules for array operations
% Also called: Hadamard Product, Schur Product and broadcast
% mutliplication
% See MATLAB function times() for help

% Given: (M x N) * (P x Q)
% For matrix multiplicaiton N must equal P and output would be (M x Q)
% 
% For element-wise array multipication the size of each array must be the
% same, or be compatible. Where compatible could be a scalar combined with
% each element of the other array, or a vector with different orientation
% that can expand to form a matrix.

a = [ 1; 2] % column vector
b = [ 3 4] % row vector

disp('matrix multiplication: a*b')
a*b
disp('Element-wise multiplicaiton: a.*b')
a.*b

c = [1 2 3; 1 2 3]
d = [2 4 6]

disp("matrix multiplication (3 X 2) * (3 X 1): c*d'")
 c*d'
disp('Element-wise multiplicaiton (3 X 2) .* (1 X 3): c.*d')
c.*d

% References: 
% https://www.mathworks.com/help/matlab/ref/times.html
% https://www.mathworks.com/help/matlab/ref/mtimes.html
% https://www.mathworks.com/help/matlab/matlab_prog/array-vs-matrix-operations.html

脚本结果:

一

 1
 2

b

 3     4

矩阵乘法:a*b

ans=

 3     4
 6     8

元素乘法:a.*b

ans=

3     4
6     8

c

 1     2     3
 1     2     3

d

 2     4     6

矩阵乘法(3×2)*(3×1):c*d'

ans=

28
28

元素乘法(3 X 2)。*(1 X 3):c.*d

ans=

 2     8    18
 2     8    18