Support for Multiplication and Transpose of Block Matrices of Symbolic Matrices?

Does MATLAB not support multiplying and transposing block symbolic matrices? For instance, the following multiplication and transpose are not evaluated on the individual matrices inside of the block matrices:

syms A B C D E F G H [2 2] matrix
X = [A B;C D].'

X = 

Y = [A B;C D]*[E F;G H]

Y = 

The outputs I am expecting are:

X = [A.' C.';B.' D.']

X = 

Y = [A*E+B*G A*F+B*H;C*E+D*G C*F+D*H]

Y = 

[ZHEN CHEN]

I have found a solution using "NCAlgebra" package of Mathematica:https://ncalgebra.github.io/#BasicMatrices.

Answer 1

[Walter Roberson]

Does MATLAB not support multiplying and transposing block symbolic matrices?

No, it does not. Most operations are postponed on symmatrix. Some operations are performed immediately though

syms A(x) [2 2] matrix
syms B [2 2] matrix
syms Z [2 2] matrix
Z(:) = 0

Z = 

X = [A B; Z A']

X(x) = 

diff(X, x)

ans(x) = 

[FingersCrossed]

Thanks, hope to see this get added in the future. I've been unable to find a competitor's software capable of doing this either, though maybe I just don't know the right syntax.

Answer 2

[Suraj]

Greetings,

Based on your inquiry, I understand that you are trying to multiply and transpose block matrices of symbolic matrices.

MATLAB does support multiplying and transposing block symbolic matrices, but I think in your example, the reason why the expected outputs are not obtained is because there is a syntax error in the matrix declaration.

When you declare the matrices A, B, C, D, E, F, G, H, you need to use the sym function instead of syms. The syms function is used for declaring multiple symbolic variables, while sym is used for declaring a single symbolic variable or a matrix of symbolic variables.

Here is a workaround for that:

% Declare symbolic matrices
A = sym('A', [2 2]);
B = sym('B', [2 2]);
C = sym('C', [2 2]);
D = sym('D', [2 2]);
E = sym('E', [2 2]);
F = sym('F', [2 2]);
G = sym('G', [2 2]);
H = sym('H', [2 2]);

% Transpose of a block matrix
X = [A B; C D].';

% Product of two block matrices
Y = [A B; C D] * [E F; G H];

% Display results
disp('X =')
disp(X)
disp('Y =')
disp(Y)

This code should give you the desired results.

Regards,

Suraj

[FingersCrossed]

Thank you for your reply, though this is not what I am trying to do. I would like to operate on A, B, C, D as symbolic matrix variables as in my example and not on an element by element basis. Examples of these operations for non-block matrices are given at:

https://www.mathworks.com/help/symbolic/use-symbolic-matrix-variables.html

[Walter Roberson]

The syms function is used for declaring multiple symbolic variables, while sym is used for declaring a single symbolic variable or a matrix of symbolic variables.

That is not correct.

The sym function is primarily intended as a function that returns a single symbolic expression without itself assigning to any variable . So sym('A', [2 2]) returns a symbolic array for whatever purpose you need; you can assign it to a variable if you want.

The syms function is primarily intended for command syntax that builds one or more symbolic expressions and assigns them to variables . So syms A [2 2] functionally does A = sym('A', [2 2]) . But syms can also create symbolic functions, such as syms f(x) and with the matrix keyword creates symmatrix

Note the difference:

syms A [2 2]
syms B [2 2] matrix
A

A = 

B

B = 

whos A B

  Name      Size            Bytes  Class        Attributes

  A         2x2                 8  sym                    
  B         2x2                 8  symmatrix              

Without the matrix keyword, the variable A becomes a matrix containing symbols A1_1, A1_2, A2_1, A2_2 whereas with the matrix keyword, B becomes a 2 x 2 symmatrix . A symmatrix is treated differently than a sym matrix:

A * magic(2)

ans = 

ans.'

ans = 

B * magic(2)

ans = 

ans.'

ans =