@Harry Garst 
dimensie_regels_voor_kronecker_en_gewone_matrices_10-5-2026.mw

Using these rules, you can determine which matrix dimensions to use and what the result of the matrix calculation will be of the dimension of the resulting matrix.

@Harry Garst 
I am interested in your code, but of course you’re keeping that to yourself :-)
Upload the existing code to the AI and ask for an educational explanation of the code, or request an explanation of how the code works for a presentation to others.
groet  Jan

matrixcalus_module_8-5-2026_.mw

It turns out that incorporating the entire factor analysis model into the module code is a step too far, and it is recommended to use Maple for this purpose instead.

The module code does contain some educational factor model commands, but they aren't suitable for real statistical work, are they?
Some improvemnents further....

@Harry Garst 
uitleg_vraag_mprimes_7-5-2026.mw

Groet Jan 

More matrix equations (polynome) to solve possible 
matrixcalus_module_7-5-2026.mw

@Harry Garst 

groeten Jan

@Harry Garst 
I tried some examples , much more need to be  tested.
matrixcalus_module_6-5-2026.mw

@Harry Garst 

I've created a MatrixCalculus module and focused on statistics as well. 
Attached a list of the features, but I have no idea if it works with real-world examples.

overzicht_mogelijkeheden_MatricCalculus_module.mw

@Harry Garst 

That doesn't surprise me at all; in Maple, too, there are ongoing developments in the mathematical topics that are implemented in the software.
That will always be the case as new mathematical knowledge is developed for theoretical or practical applications

AI is a great tool for researchers to ask questions.

I’ve also been working on that VEC operator and created a module for it that works structurally the same way as the Kronecker module.
I have no idea what the application is yet, but Kronecker products are also used in it.
Just for curosity. 

Groeten Jan

@Harry Garst 
I can do that for public use, why  not?

 groeten  Jan

How do I evaluate a simplified expression and determine the dimension matrix from module code?

kroneckerproducts_module_with_dimensioncheckDEF_5-5-2026_.mw

Examine the mixed Kronecker expression ?
kroneckerproducts_module_with_dimensioncheck__4-5-2026.mw

Module has dimensioncheck for numeric use and symbolic use a dimension warning

Check this in Linear Algebra 
Your example is correct , because  X and Y do have the right dimensions

Experiment with dimensions  

restart;
with(LinearAlgebra):

# =========================================================
# Kies afmetingen zodat de regel geldt:
#   X is een kolomvector (n×1)
#   Y is een rijvector   (1×m)
# =========================================================
# A : p × n          (p willekeurig)
# X : n × 1          (kolomvector)
# Y : 1 × m          (rijvector)
# B : m × q          (q willekeurig)
p := 3;
n := 2;
m := 4;
q := 2;

A := Matrix(p, n, symbol = a);
X := Matrix(n, 1, symbol = x);
Y := Matrix(1, m, symbol = y);
B := Matrix(m, q, symbol = b);

# Linker- en rechterlid van de identiteit
L := A . (KroneckerProduct(X, Y)) . B;
R := KroneckerProduct(A . X, Y . B);

# Verschil (moet een nulmatrix zijn)
Verschil := simplify(L - R);
print(Verschil);

@Harry Garst 

This mixed Kronecker expression is a special case; the same seems to apply to the module code
The module code does not yet check the dimensions of the simplified expressions, but it could.(i  add this later)

The question you’re asking is a tricky one, but hopefully this answer will be helpful
You can use the procedure to check the input for dimensions, and with this knowledge, you can also check this in a linear algebra package.

gemixed_produkt_expressie_voorwaarden_dimensie_controle_en_uitleg_3-5-2026.mw

@Harry Garst 

You try to check rule 7 ...
I used the Kron notation, easier to read

Download vraag-_Is_this_correct_mprimes_3-5-2026.mw