A matrix times a vector whose elements are matrix too.

Here, we use a matrix Sx times a vector initialvector whose elements are also matrix, the code is in the following. And we expect Sx*initialvector could give a matrix with size [5*5; 5*5; 5*5], similar with initialvector. What should we do?

Sx=1/sqrt(2)*[0 1 0; 1 0 1; 0 1 0];
initialu1=rand(5);
initialu0=rand(5);
initialuminus1=rand(5);
initialvector=[initialu1; initialu0; initialuminus1;];
Sx*initialvector

Added: Take a very simple example, if the elements initialu1, initialu0 and initialuminus1 are just scalar numbers, we calculate

ones(3)*initialvector

which should give

[initialu1+initialu0+initialuminus1; initialu1+initialu0+initialuminus1; initialu1+initialu0+initialuminus1]

However, initialu1, initialu0 and initialuminus1 are matrix here. But we still want the reslut

[initialu1+initialu0+initialuminus1; initialu1+initialu0+initialuminus1; initialu1+initialu0+initialuminus1]

which is a matrix now, and whose size is same with initialvector...

[dpb]

No combination of sizes/elements matches anything by which to do any normally defined array operations; either on an element-by-element basis nor with matrix multiplication.

You'll have to make up something -- we have no way to even guess what the intent might be, and with no context as to what the arrays might represent, couldn't even hypothesize some reason for even thinking there should be any such thing.

[Wang]

@dpb Thank you! And more explanations are added in the question.

[Steven Lord]

How do you get from:

% ones(3)*initialvector

to

% initialu1+initialu0+initialuminus1

Let's take a concrete example of an initial vector that contains scalars.

initialvector = [1; 2; 4];
result = ones(3)*initialvector

result = 3×1

7 7 7

The result is a 3-by-1 vector, the same size as initialvector. Each element of result is the sum of the elements of initialvector, but how are you collapsing that vector to the scalar value resulting from summing the elements of initialvector?

And if we had a different matrix:

result2 = [0 1 0; 1 0 1; 0 1 0]*initialvector

result2 = 3×1

2 5 2

How specifically would you collapse that vector into a scalar? Is the expected result 3, 5, 2, or something else entirely?

mean(result2)

ans = 3

max(result2)

ans = 5

min(result2)

ans = 2

result2(1)

ans = 2

[Wang]

@Steven Lord Sorry about that. I made a mistake. And the question is updated.

What I want to say is that there is no collapse. For example, if initialvector is a matrix,like

initialvector=[ones(5); ones(5); ones(5);];

The desired answer of ones(3)*initialvector should be

[3*ones(5); 3*ones(5); 3*ones(5);]

Answer 1

[Steven Lord]

a vector initialvector whose elements are also matrix

That doesn't exist in MATLAB, at least not if you want initialvector to be a numeric vector. Your initialvector isn't a vector, it's a matrix.

You could make a cell array that is a vector and have each cell in the cell array contain a matrix, but multiplication is not defined for cell arrays.

c = {magic(5), ones(5), rand(5)}

c = 1×3 cell array
    {5×5 double}    {5×5 double}    {5×5 double}

isvector(c)

ans = logical
   1

Even if you used c and indexed into it to extract the matrices stored in each cell, matrix multiplication between a 3-by-3 matrix and a 5-by-5 matrix is not mathematically defined. But from the structure of that Sx matrix I wonder if maybe you're trying to do some type of convolution or filtering. If so conv2 or filter2 might be what you're looking for.

Sx=1/sqrt(2)*[0 1 0; 1 0 1; 0 1 0];
M = magic(5);
conv2(M, Sx, 'same')

ans = 5×5

33.2340 16.2635 27.5772 21.2132 16.9706 18.3848 42.4264 23.3345 36.0624 36.0624 27.5772 24.0416 36.7696 49.4975 27.5772 19.0919 37.4767 50.2046 31.1127 36.7696 19.7990 33.9411 27.5772 38.8909 3.5355

[Wang]

Thanks for your patience @Steven Lord! Some explanations are added in the question. Hope it's clear.