Multiple a matrix by every column of another matrix and stack the results in some form

Hello, I have a matrix A: 3xn and a matrix B: 3x6. What I wish to do is subtract each column of B from A as follows:

B_11 is subtracted from A_1i for i = 1:n, B_21 is subtracted from A_2i for i = 1:n, B_31 is subtracted from A_3i for i = 1:n.

This is repeated for each column of B with the whole A matrix and the results stacked each time, giving a resultant matrix that's 18xn.

Or storing the 3xn matrices for the 6 different B columns in a structure is also okay.

I have tried combinations of repmat but nothing useful yet. Can we do this without a loop, preferably?

Answer 1

[Voss]

I think this will do it:

n = 10;
A = 100+2*reshape(1:3*n,3,[])

A = 3×10

102 108 114 120 126 132 138 144 150 156 104 110 116 122 128 134 140 146 152 158 106 112 118 124 130 136 142 148 154 160

B = reshape(1:3*6,3,[])

B = 3×6

1 4 7 10 13 16 2 5 8 11 14 17 3 6 9 12 15 18

new_A = repmat(A,size(B,2),1);
new_B = repmat(B(:),1,size(A,2));
result = new_A-new_B;
disp(result);

   101   107   113   119   125   131   137   143   149   155
   102   108   114   120   126   132   138   144   150   156
   103   109   115   121   127   133   139   145   151   157
    98   104   110   116   122   128   134   140   146   152
    99   105   111   117   123   129   135   141   147   153
   100   106   112   118   124   130   136   142   148   154
    95   101   107   113   119   125   131   137   143   149
    96   102   108   114   120   126   132   138   144   150
    97   103   109   115   121   127   133   139   145   151
    92    98   104   110   116   122   128   134   140   146
    93    99   105   111   117   123   129   135   141   147
    94   100   106   112   118   124   130   136   142   148
    89    95   101   107   113   119   125   131   137   143
    90    96   102   108   114   120   126   132   138   144
    91    97   103   109   115   121   127   133   139   145
    86    92    98   104   110   116   122   128   134   140
    87    93    99   105   111   117   123   129   135   141
    88    94   100   106   112   118   124   130   136   142