Matrix Multiplication , Tensor Product of Matrices , Matrix transpose and Sub-Matrices

I already asked a part of this question before, but the topic changed now. It's not homework. I want to find all possible combinations of four basis vectors (dimension = 4), depending on the user input. Repetition should be allowed.

I.e. lets call the vectors 0, 1, 2 and 3.

If the User enters N=3, the combinations can be:

000 001 002 . . . 333

The application should store each combination separately in a (4xN) Matrix. And cout each Matrix.

For example, if:

"0" is associated with the 4x1 Matrix [column-vector] (0,0,0,0)

"1" with (0,0,0,1)

"2" with (0,0,1,0)

"3" with (0,1,0,0)

the possible combination "000" should be stored in the 4x3 Matrix

0 0 0

0 0 0

0 0 0

0 0 0

and this Matrix should be streamed out to the screen.

Moreover the tensor product of every (4x1) Matrix in each of these matrices should be calculated and stored.

In the given example ("x" means tensor product):

0 x 0 x 0

.

.

.

3 x 3 x 3

has to be computed and stored separately, since I also need the transpose of these product-matrices.

Another point is, I have to initialize a 2x2 Sub-Matrix in a given p x 2 Matrix.

For this application, I don't want to use a matrix library and I am looking for a fast and efficient way, because the size of the matrices grows exponentially.

Since I am absolutely new to C++, I have no clue, how to code this without a library. I know, it must be something with the STL Container vector, but I am not familiar with it.

Thanks for your help,

Kepler