public static int Test_UnitVector_Multiply_ElementaryMatrix()
{
/*
* e'r * Eij = e'r * ei * e'j = &ri *e'j where & = Kronecker delta
*
*/
StringBuilder sb = new StringBuilder();
ElementaryMatrix E12 = new ElementaryMatrix(4, 4, "E12"); // 4 x 4 ElementaryMatrix
UnitVector e1 = new UnitVector("e1", 4); //Order four unit vector e1
UnitVector e2 = new UnitVector("e2", 4, RowColumn.Row); //Order four row unit vector e2
UnitVector er = new UnitVector("e3", 4, RowColumn.Row); //Order four unit row vector e3 our er above
/*
* i = 1, j = 2, r = 3
*/
sb.Append(@"e'_rE_{ij} = e'_re_ie'_j = \delta_{r j}e'j \\");
//Test matrix unit vector * Elementary Matrix, er * Eij
UnitVector uvE1 = er * E12;
sb.Append(@"e'_3E_{12} = " + uvE1.ToLatex() + @"\;");
//Test e'r * ei * e'j
UnitVector uvE2 = er * e1 * e2;
sb.Append(@"e'_3e_1e'_2 = " + uvE2.ToLatex() + @"\;");
//Test &ri * e'j
UnitVector uvE3 = UnitVector.KroneckerDelta(3, 1) * e2;
sb.Append(@" \delta_{3 1}e_2 = " + uvE3.ToLatex() + @" \tag{1}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_UnitVector_Multiply_ElementaryMatrix.html"); //display Latex via mathjax
return(0);
}
public static int Test_ElementaryMatrix_Multiply_UnitVector()
{
/*
* Eij * er = ei*e'j*er = &jr *ei where & = Kronecker delta
*
*/
StringBuilder sb = new StringBuilder();
ElementaryMatrix E12 = new ElementaryMatrix(4, 4, "E12"); // 4 x 4 ElementaryMatrix
UnitVector e1 = new UnitVector("e1", 4); //Order four unit vector e1
UnitVector e2 = new UnitVector("e2", 4, RowColumn.Row); //Order four row unit vector e2
UnitVector er = new UnitVector("e3", 4); //Order four unit vector e3 our er above
/*
* i = 1, j = 2, r = 3
*/
//Test matrix * unit vector, Eij * er
UnitVector uvE1 = E12 * er;
sb.Append(@"E_{12}e_3 = " + uvE1.ToLatex() + @"\;");
//Test e1* e'j * er
UnitVector uvE2 = e1 * e2 * er;
sb.Append(@"e_1e'_2e_3 = " + uvE2.ToLatex() + @"\;");
//Test &jr * ei
UnitVector uvE3 = UnitVector.KroneckerDelta(2, 3) * e1;
sb.Append(@" \delta_{2 3}e_1 = " + uvE3.ToLatex());
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_ElementaryMatrix_Multiply_UnitVector.html"); //display Latex via mathjax
return(0);
}