public string ImBasis()
{
MyMatrix row_echelon = Clone();
string output = row_echelon.GaussLaTeX(revert: false) + '\n';
LaTeXExport export = new LaTeXExport(1, ",", 1, false, "$$\\text{Im basis}:\\ ");
for (int i = 0; i < n; i++)
{
int j_s = 0;
for (; j_s < m && row_echelon[i, j_s] == 0; j_s++)
{
;
}
if (j_s >= m)
{
break;
}
export.Add(GetColumn(j_s).GetLaTeX());
}
if (export.Empty)
{
export.Add(GetColumn(0).GetLaTeX());
}
return(output + export.Result);
}
public string KerBasis()
{
MyMatrix row_echelon = Clone();
string output = row_echelon.GaussLaTeX() + '\n';
LaTeXExport export = new LaTeXExport(1, ",", 1, false, "$$\\ker\\ \\text{basis}:\\ ");
List <int> pivots = new List <int>();
for (int i = 0; i < n; i++)
{
int j_s = 0;
for (; j_s < m && row_echelon[i, j_s] == 0; j_s++)
{
;
}
if (j_s >= m)
{
break;
}
pivots.Add(j_s);
}
int j_free = 0;
for (int j = 0; j < m - pivots.Count; j++, j_free++)
{
for (; pivots.Contains(j_free); j_free++)
{
;
}
MyMatrix basis_el = new MyMatrix(m, 1);
basis_el[j_free, 0] = 1;
for (int i = 0; i < pivots.Count; i++)
{
basis_el[pivots[i], 0] = -row_echelon[i, j_free];
}
export.Add(basis_el.GetLaTeX());
}
if (export.Empty)
{
export.Add(new MyMatrix(m, 1).GetLaTeX());
}
return(output + export.Result);
}
public string InverseLaTeX()
{
if (!IsSquare)
{
throw new InvalidOperationException("Matrix is not square!");
}
if (Determinant == 0)
{
throw new DivideByZeroException("Determinant zero!");
}
MyMatrix tmp = new MyMatrix(n, n * 2);
tmp.Set(this);
for (int i = 0; i < n; i++)
{
tmp[i, i + n] = 1;
}
string output = tmp.GaussLaTeX(n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
tmp[i, j] = tmp[i, j + n];
}
}
tmp.M = n;
/*try
* {
* if (!(tmp * this).Equals(Id))
* throw new Exception();
* }
* catch { throw new ArithmeticException("Cannot find inverse matrix!"); }*/
values = tmp.values;
return(output);
}