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change

make_matrix(x, y, default)

to

make_matrix_by_default(x, y, default = T())

This makes better error messages for failures like:

make_matrix(x, y, function) // ops, I did mean make_matrix_by_function!

The information about value_type, cols and rows is only needed for implicit initialization with an array. If the array have been explicit defined, then can the compiler extract the information from the parameter:

int data[2][2] = {{0, 1}, {2, 3}};
make_matrix(data); // same as make_matrix< int >(2_C, 2_R, d)

Instead of making the underlaying matrix-type a template parameter, define a type-trait for matrix types and use enable_if to enable the algorithms.

(This is a spontaneous idea, don't know if it will work!)

Use std::unique_ptr instead of boost::container::vector.

-> less dependencies

std::is_default_constructible
std::is_copy_constructible
std::is_move_constructible

…

#include <iostream>

struct A{};
struct B{};

struct dim: private A, private B{};

struct C: dim{ int v; };

int main(){
    std::cout << sizeof(A) << std::endl;
    std::cout << sizeof(B) << std::endl;
    std::cout << sizeof(dim) << std::endl;
    std::cout << sizeof(C) << std::endl;
}

Output:
1
1
1
4

std::invoke is not constexpr.

separate ct dims from dim args and array dims and compare them by static_assert