What are the factors that you want to use? An obvious solution is to multiply the "elongated diagonal matrix" by the identity matrix...
I know this question sounds a bit weird but it basically comes down to this. I want to create a matrix of this type:
How do I produce such a matrix, using only matrix multiplication? I've tried a lot of things myself but my understanding of matrix algebra is too limited to "see" how it can be done. Ideally, I would like a general formula where I can specify the amount of columns and the amount of repetitions (1's) in each column. For instance, 2 repeats and 4 columns:
Anyone has suggestions?
Well if you know Basic, easy enough:
u = repeats, v = columns, w = rows
100 GET u, v
110 w = u * v
120 DIM a(w,v) 'set up array/matrix
130 FOR c = 1 TO v
140 FOR r = c * u - u + 1 TO c * u
150 a(r,c) = 1
160 NEXT r
170 NEXT c
180 FOR r = 1 TO w
190 FOR c = 1 TO v
200 PRINT a(r,c)
210 NEXT c
220 NEXT r
If repeats = 5 and colums = 3, this will print:
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 0 1
0 0 1
0 0 1
0 0 1
0 0 1