// get matrix (n^2 size ! , 1-s on main diagonal 0 elsewhere), multiply with itself, if result is identical to original TRUE, else FALSE.
public static void IsIdentity(int[,] inMatrix)
{
string askIsIt = "\nIs The Matrix likely to be an \"Identity Matrix\"?";
int idRows = inMatrix.GetLength(0); int idCols = inMatrix.GetLength(1);
int[,] identity = new int[idRows, idCols];
double s = Math.Sqrt(idRows * idCols);
Console.WriteLine($"-------------------------\n" +
"Identity Matrix check\n----------\n" +
$"Row length (nr. of columns): {idCols}\n" +
$"Column length (nr. of rows): {idRows}\n" +
$"This one's square root: {s}");
// FIRST - an IM is a matrix with equal length rows and columns.
if (idRows == s && idCols == s)
{
Console.Write($"{askIsIt} May be {true}.");
// SECOND - an IM on the power of 2 (basically multiplied ONCE with itself) ia always identical to the one being evaluated!
MakeIdentity(inMatrix, identity);
Console.WriteLine("\n\nThe Matrix, Origins:"); SetPrint.PrintTheMatrix(inMatrix);
Console.WriteLine("\nThe Matrix, Squared:"); SetPrint.PrintTheMatrix(identity);
Console.WriteLine($"\nIs \"The Matrix\" an \"Identity Matrix\"? {VerifyIdentity(inMatrix, identity)}.");
}
else
{
Console.Write($"{askIsIt} Definitely {false}.\n" +
$"Such a matrix has to be square (equal length rows & columns) to even be considered.\n");
}
}
static void Main(string[] args)
{
int cols = SetPrint.DefineTheMatrixLimits("Row length (nr. of columns) = ");
int rows = SetPrint.DefineTheMatrixLimits("Column length (nr. of rows) = ");
string askMatrix = "\n\tEnter The Matrix:\n--------------------------";
int[,] theMatrix = new int[rows, cols];
SetPrint.GetTheMatrix(askMatrix, theMatrix);
SetPrint.PrintTheMatrix(theMatrix);
GetDiagonal.FindSecondaryDiagonal(theMatrix);
SetPrint.PrintTheMatrix(GetTransposed.TransposeMatrix(theMatrix));
CheckIdentity.IsIdentity(theMatrix);
Console.WriteLine("\nEnd.\n");
}