public Matrix<T> getKernelBasis() {
Matrix<T> reducedRowEchelonForm = getReducedRowEchelonForm();
boolean[] hasLeadingOne = new boolean[n];
List<Integer> indices = new ArrayList<Integer>();
int j = 0;
for (int i = 0; i < m; i++)
while (j < n) {
T aij = reducedRowEchelonForm.get(i, j);
if (!aij.equals(zero)) {
if (!aij.equals(one)) throw new Error();
indices.add(j);
hasLeadingOne[j] = true;
j++;
break;
}
j++;
}
InvertibleBinaryOperation<T> addition = ring.addition();
Matrix<T> kernelBasis = new Matrix<T>(ring, n, n - indices.size());
kernelBasis.zero();
int k = 0;
for (int i = 0; i < n; i++)
if (!hasLeadingOne[i]) {
kernelBasis.set(i, k, one);
for (int l = 0; l < indices.size(); l++)
kernelBasis.set(indices.get(l), k, addition.inverse(reducedRowEchelonForm.get(l, i)));
k++;
}
if (k != kernelBasis.n) throw new Error(k + " / " + indices.size());
return kernelBasis;
}
public void identity() {
if (m != n) throw new Error();
zero();
for (int i = 0; i < n; i++) matrix[i][i] = one;
}