public static RationalSquareMatrix FaddevasMethod(RationalSquareMatrix AIn, out RationalVector CharacteristicEquation)
{
RationalSquareMatrix A = AIn.Clone();
CharacteristicEquation = new RationalVector();
RationalSquareMatrix A_n = A;
Rational b_n = 1;
RationalSquareMatrix B_n = null;
RationalSquareMatrix I = null;
RationalSquareMatrix AInv = null;
int i = 0;
for (i = 1; i < A.Rows; i++)
{
b_n = -A_n.Trace() / (i);
CharacteristicEquation.Add(b_n);
I = RationalSquareMatrix.IdentityMatrix(A.Rows);
B_n = A_n + b_n * I;
A_n = A * B_n;
}
b_n = -A_n.Trace() / (i);
CharacteristicEquation.Add(b_n);
AInv = -1 / b_n * B_n;
AInv.FullRep = A.ToLatex() + "^{-1} = " + AInv.ToLatex();
return(AInv);
}
public static int Test_EMatrix()
{
RationalFactory rf = new RationalFactory();
RationalSquareMatrix I = RationalSquareMatrix.IdentityMatrix(3);
RationalSquareMatrix ACopy = rf[3, 3,
"1", "2", "-2",
"-1", "1", "3",
"2", "-1", "2"
];
RationalSquareMatrix ACopy2 = rf[3, 3,
"-7", "2", "-2",
"-3", "1", "3",
"8", "-1", "2"
];
RationalSquareMatrix ACopy3 = rf[4, 4,
"4", "7", "2", "3",
"1", "3", "1", "2",
"2", "5", "3", "4",
"1", "4", "2", "3"
];
string ll = RationalSquareMatrix.DetFullRep(ACopy);
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(ll, "Test_EMatrix.html"); //display Latex via mathjax
return(0);
}