decompose matrix into product of sparse matrix
This decomposition method creates a sequence of sparce
matrix, many just the indentity matrix with one or two additional
entries. Each additional matrix uses the previous matricies and
products of previous matricies.

At the end, the inverse of the sequence of matrix become
the product equal to the initial materix. The matricies
in the product could be grouped into two or more matrix
such that the product is the initial matrix.

Source code for java version, one example
decomp2.java source
decomp2_java.out result

Source code for python version, one example
decomp2.java source
decomp2_py.out result


Source code for java version, general for 3 by 3
decomp3.java source
decomp3_java.out result

Source code for python version, general for 3 by 3
decomp3.py source
decomp3_py.out result

Source code for python3 version, general for 3 by 3
decomp3.py3 source
decomp3_py3.out result

for various A matrix:

Source code for java version, general for 3 by 3
decomp3a.java source
decomp3a_java.out result

Source code for java version, general for 3 by 3 with negative
decomp3b.java source
decomp3b_java.out result

Source code for java version, general for 3 by 3 with negative
decomp3c.java source
decomp3c_java.out result


An n by n matrix could have about  n^2-n  sparse matix in the product.

last updated  8/26/2019