Multiplication of Array of Matrices with Array of scalars

Hello, can anyone help me ? I did some operations with scalar matrix: Example:

    A= [1 2 3 4 5];
    C= [0.5  0.25 0 0 0.25; 0.25 0.5 0.25 0 0; 0 0.25 0.5 0.25 0; 0 0 0.25 0.5 0.25; 0.25  0 0 0.25 0.5];
    A*C=[ 2.25   2  3  4    3.75];  %  usual in matrix multiplication

Now my task is to change A elements into 2x2 matrices and then to do the same operation, for example, C is the same matrix:

AA= [ [1.75 4;-0.25 -0.25]  [1.55 4;-0.25 -0.45]  [1.75  4;-0.25  -0.25 ] [1.65  4;-0.25 -0.35]  [1.15  4;-0.25 -0.85]];
                     % I construct this as a cell array AA is  cell 1x5, where each variable is a 2x2 matrix

I want to multiply each variable in a cell array (which is a 2x2 matrix) coefficients in C, if to make clear, the multiplication should be performed like this;

   AA*C = [ [1.75 4;-0.25 -0.25]*0.5+ [1.55 4;-0.25 -0.45] *0.25+0+0+[1.15  4;-0.25 -0.85]*0.25  
            [1.75 4;-0.25 -0.25]*0.25 +[1.55 4;-0.25 -0.45]*0.5+ [1.75  4;-0.25  -0.25 ]*0.25+0+0
             0+[1.55 4;-0.25 -0.45] *0.25+[1.75  4;-0.25  -0.25 ]*0.5+[1.65  4;-0.25 -0.35]*0.25+0
             0+0+[1.75  4;-0.25  -0.25 ]*0.25+[1.65  4;-0.25 -0.35]*0.5+[1.15  4;-0.25 -0.85]*0.25
             [1.75 4;-0.25 -0.25] *0.25 +0+0+[1.65  4;-0.25 -0.35]*0.5+[1.15  4;-0.25 -0.85]*0.25 ];

How can I get this – to preserve usual matrix operation? Thank You.

[Stephen Cobeldick]

"I did some operations with scalar matrix"

A scalar matrix would have size 1x1x1x1x..., but I don't see any matrices in your code with that size. What are you referring to?

[Rasa Smith]

Hello, I mean I have usual matrices A(1x5) and C(5x5) (in my real task it is not 5 but e.g. 10000). I multiply A*C as usual, the product A*C has format 1x5. In my real task I want to multiply AA (format 1x5 - which is a matrix of five matrices of format 2x2) by the same C (format 5x5) so that the product produces the result - 1x5 format matrix where each element is a 2x2 matrix. In other words, the task I want to perform has to give me a result - multiplication as matrix by scalar and then to sum, e.g. the first element of AA*C should be calculated:

[1.75 4;-0.25 -0.25]*0.5 +
[1.55 4;-0.25 -0.45]*0.25+
[1.75  4;-0.25  -0.25 ]*0+
[1.65  4;-0.25 -0.35]*0+
[1.15  4;-0.25 -0.85]*0.25 

 Then in my case the product of AA*C should be:
[ [1.55  4;  -0.25   -0.45]
  [1.65  4;  -0.25   -0.35]
  [1.675 4;  -0.25  -0.325]
  [1.55  4;  -0.25  -0.45]
  [1.425 4;  -0.25  -0.575] ];

I hope I made it more easy to understand:) Thank you.

Answer 1

[Ahmet Cecen]

I believe you are over-complicating your problem by thinking as if you are working things out on a board. Your operation is separable and doesn't need you to store things in a cell array or represent them as matrices. From the exact assignment of AA in your question as an array:

AA = reshape(AA, 4,5);

Now each of your "matrices" is a column. Where:

AA*C(1,:)'

will give you first row of AA*C. If you have to return a matrix:

reshape(AA*C(1,:)',2,2);

Now you can loop over this to solve your problem. You can also store C as a cell instead and use cellfun, but shouldn't be necessary in your case.