Func _Matrix_AddColumnToMatrixColumn($aMatrix, $aColumn, $dColumn)
	If (UBound($aMatrix) = UBound($dColumn)) Then
		Local $returnMatrix = $aMatrix
		For $row = 0 To UBound($aMatrix) - 1 Step 1
			$returnMatrix[$row][$dColumn] += $aColumn[$row][0]
		Next
		Return $returnMatrix
	EndIf
	Return -1
EndFunc   ;==>_Matrix_AddColumnToMatrix
Func _Matrix_AddRowToMatrixRow($aMatrix, $aRow, $dRow)
	If (UBound($aMatrix, 2) = UBound($aRow, 2)) Then
		Local $returnMatrix = $aMatrix
		For $column = 0 To UBound($aMatrix, 2) - 1 Step 1
			$returnMatrix[$dRow][$column] += $aRow[0][$column]
		Next
		Return $returnMatrix
	EndIf
	Return -1
EndFunc   ;==>_Matrix_AddRowToMatrix
Func _Matrix_AddMatrix($aMatrix1, $aMatrix2)
	If (UBound($aMatrix1) = UBound($aMatrix2)) And (UBound($aMatrix1, 2) = UBound($aMatrix2, 2)) Then
		Local $returnMatrix = $aMatrix1
		For $row = 0 To UBound($aMatrix1) - 1 Step 1
			For $column = 0 To UBound($aMatrix1, 2) - 1 Step 1
				$returnMatrix[$row][$column] += $aMatrix2[$row][$column]
			Next
		Next
		Return $returnMatrix
	EndIf
	Return -1
EndFunc   ;==>_Matrix_AddMatrix
Func _Matrix_ExtractRow($aMatrix, $mRow)
	If ($mRow < UBound($aMatrix)) Then
		Local $returnRow[1][UBound($aMatrix, 2)]
		For $column = 0 To UBound($aMatrix, 2) - 1 Step 1
			$returnRow[0][$column] = $aMatrix[$mRow][$column]
		Next
		Return $returnRow
	EndIf
	Return -1
EndFunc   ;==>_Matrix_ExtractRow
Func _Matrix_ExtractColumn($aMatrix, $mColumn)
	If ($mColumn < UBound($aMatrix, 2)) Then
		Local $returnColumn[UBound($aMatrix)][1]
		For $row = 0 To UBound($aMatrix) - 1 Step 1
			$returnColumn[$row][0] = $aMatrix[$row][$mColumn]
		Next
		Return $returnColumn
	EndIf
	Return -1
EndFunc   ;==>_Matrix_ExtractColumn
Func _Matrix_GetCofactorMatrix($aMatrix)
	If UBound($aMatrix) = UBound($aMatrix, 2) Then
		Local $returnMatrix[UBound($aMatrix)][UBound($aMatrix)]
		For $row = 0 To UBound($aMatrix) - 1 Step 1
			For $column = 0 To UBound($aMatrix) - 1 Step 1
				$returnMatrix[$row][$column] = (Mod($row + $column, 2) = 0 ? 1 : (-1)) * _Matrix_GetDeterminantGauss(_Matrix_RemoveRowAndColumn($aMatrix, $row, $column))
			Next
		Next
		Return $returnMatrix
	EndIf
	Return -1
EndFunc   ;==>_Matrix_GetCofactorMatrix
Func _Matrix_GetAdjugateMatrix($aMatrix)
	Return _Matrix_TransposeMatrix(_Matrix_GetCofactorMatrix($aMatrix))
EndFunc   ;==>_Matrix_GetAdjugateMatrix
Func _Matrix_GetDeterminantLaPlace($aMatrix)
	If UBound($aMatrix) = UBound($aMatrix, 2) Then
		Local $returnDet = 0
		If UBound($aMatrix) = 3 Then
			Local $tempAdd, $tempSub
			For $startColumn = 0 To 2 Step 1
				$tempAdd = 1
				$tempSub = 1
				For $row = 0 To 2 Step 1
					$tempAdd *= $aMatrix[$row][Mod($startColumn + $row, 3)]
					$tempSub *= $aMatrix[2 - $row][Mod($startColumn + $row, 3)]
				Next
				$returnDet += $tempAdd - $tempSub
			Next
			Return $returnDet
		EndIf
		If UBound($aMatrix) = 2 Then
			Return $aMatrix[0][0] * $aMatrix[1][1] - $aMatrix[1][0] * $aMatrix[0][1]
		EndIf
		If UBound($aMatrix) = 1 Then
			Return $aMatrix[0]
		EndIf
		;Matrix Größer 3 -> Laplace Entwicklungssatz
		For $column = 0 To UBound($aMatrix) - 1 Step 1
			$returnDet += (Mod($column, 2) = 0 ? 1 : (-1)) * $aMatrix[0][$column] * _Matrix_GetDeterminantLaPlace(_Matrix_RemoveRowAndColumn($aMatrix, 0, $column))
		Next
		Return $returnDet
	EndIf
	Return 0
EndFunc   ;==>_Matrix_GetDeterminantLaPlace
Func _Matrix_GetInverseMatrixWithAdjugate($aMatrix)
	Local $Determinant = _Matrix_GetDeterminantGauss($aMatrix)
	If $Determinant = 0 Then Return -1
	Return _Matrix_MultiplyWithScalar(_Matrix_GetAdjugateMatrix($aMatrix), 1 / $Determinant)
EndFunc   ;==>_Matrix_GetInverseMatrix
Func _Matrix_GetDeterminantGauss($aMatrix)
	If UBound($aMatrix) = UBound($aMatrix, 2) Then
		Local $determinantMultiplier = 1
		Local $signum = 0
		Local $returnMatrix = $aMatrix
		Local $workingColumn = 0
		Local $addRow, $addRowCopy
		Local $isZero = False
		For $workingRow = 0 To UBound($returnMatrix) - 1 Step 1
			$isZero = True
			For $actualRow = $workingRow To UBound($returnMatrix) - 1 Step 1
				If ($returnMatrix[$actualRow][$workingColumn] <> 0) Then
					If ($actualRow <> $workingRow) Then
						$signum += 1
						$returnMatrix = _Matrix_SwapRows($returnMatrix, $actualRow, $workingRow)
					EndIf
					$determinantMultiplier *= $returnMatrix[$workingRow][$workingColumn]
					$returnMatrix = _Matrix_MultiplyRowWithScalar($returnMatrix, $workingRow, 1 / $returnMatrix[$workingRow][$workingColumn])
					$isZero = False
					ExitLoop
				EndIf
			Next
			If ($isZero) Then Return 0
			$addRow = _Matrix_ExtractRow($returnMatrix, $workingRow)
			$addRowCopy = $addRow
			For $actualRow = $workingRow + 1 To UBound($returnMatrix) - 1 Step 1
				If ($returnMatrix[$actualRow][$workingColumn] <> 0) Then
					$addRow = _Matrix_MultiplyWithScalar($addRow, (-1) * $returnMatrix[$actualRow][$workingColumn])
					$returnMatrix = _Matrix_AddRowToMatrixRow($returnMatrix, $addRow, $actualRow)
					$addRow = $addRowCopy
				EndIf
			Next
			$workingColumn += 1
		Next
		Return $determinantMultiplier * (Mod($signum, 2) = 1 ? -1 : 1)
	EndIf
	Return 0
EndFunc   ;==>_Matrix_GetDeterminantGauss
Func _Matrix_MultiplyRowWithScalar($aMatrix, $mRow, $mScalar)
	If $mRow < UBound($aMatrix) Then
		Local $returnMatrix = $aMatrix
		For $column = 0 To UBound($aMatrix, 2) - 1 Step 1
			If ($returnMatrix[$mRow][$column] <> 0) Then
				$returnMatrix[$mRow][$column] *= $mScalar
			EndIf
		Next
		Return $returnMatrix
	EndIf
	Return -1
EndFunc   ;==>_Matrix_MultiplyRowWithScalar
Func _Matrix_MultiplyColumnWithScalar($aMatrix, $mColumn, $mScalar)
	If $mColumn <= UBound($aMatrix, 2) - 1 Then
		Local $returnMatrix = $aMatrix
		For $row = 0 To UBound($aMatrix) - 1 Step 1
			If ($returnMatrix[$row][$mColumn] <> 0) Then
				$returnMatrix[$row][$mColumn] *= $mScalar
			EndIf
		Next
		Return $returnMatrix
	EndIf
	Return -1
EndFunc   ;==>_Matrix_MultiplyColumnWithScalar
Func _Matrix_MultiplyWithScalar($aMatrix, $mScalar)
	Local $returnMatrix = $aMatrix
	For $row = 0 To UBound($aMatrix) - 1 Step 1
		For $column = 0 To UBound($aMatrix, 2) - 1 Step 1
			If ($returnMatrix[$row][$column] <> 0) Then
				$returnMatrix[$row][$column] *= $mScalar
			EndIf
		Next
	Next
	Return $returnMatrix
EndFunc   ;==>_Matrix_MultiplyWithScalar
Func _Matrix_MultiplyWithMatrix($aMatrix1, $aMatrix2)
	If (UBound($aMatrix1, 2) = UBound($aMatrix2)) Then
		Local $returnMatrix[UBound($aMatrix1)][UBound($aMatrix2, 2)]
		For $newRow = 0 To UBound($returnMatrix) - 1 Step 1
			For $newColumn = 0 To UBound($returnMatrix, 2) - 1 Step 1
				Local $newValue = 0
				For $i = 0 To UBound($aMatrix1) - 1 Step 1
					$newValue += $aMatrix1[$newRow][$i] * $aMatrix2[$i][$newColumn]
				Next
				If ($newValue = -(0.0)) Then $newValue = 0
				$returnMatrix[$newRow][$newColumn] = $newValue
			Next
		Next
		Return $returnMatrix
	EndIf
	Return -1
EndFunc   ;==>_Matrix_MultiplyWithMatrix
Func _Matrix_RemoveRowAndColumn($aMatrix, $mRow, $mColumn)
	If ($mRow < UBound($aMatrix)) And ($mColumn < UBound($aMatrix, 2)) Then
		Local $returnMatrix[UBound($aMatrix) - 1][UBound($aMatrix, 2) - 1]
		For $row = 0 To UBound($returnMatrix) - 1 Step 1
			For $column = 0 To UBound($returnMatrix, 2) - 1 Step 1
				$returnMatrix[$row][$column] = $aMatrix[$row + ($row >= $mRow ? 1 : 0)][$column + ($column >= $mColumn ? 1 : 0)]
			Next
		Next
		Return $returnMatrix
	EndIf
	Return -1
EndFunc   ;==>_Matrix_RemoveRowAndColumn
Func _Matrix_SubstractMatrix($aMatrix1, $aMatrix2)
	Return _Matrix_AddMatrix($aMatrix1, _Matrix_MultiplyWithScalar($aMatrix2, (-1)))
EndFunc   ;==>_Matrix_SubstractMatrix
Func _Matrix_SwapRows($aMatrix, $mRow1, $mRow2)
	If ($mRow1 = $mRow2) Then Return $aMatrix
	If ($mRow1 < UBound($aMatrix)) And ($mRow2 < UBound($aMatrix)) Then
		Local $returnMatrix = $aMatrix
		Local $tempVal = 0
		For $column = 0 To UBound($aMatrix, 2) - 1 Step 1
			$tempVal = $aMatrix[$mRow1][$column]
			$returnMatrix[$mRow1][$column] = $returnMatrix[$mRow2][$column]
			$returnMatrix[$mRow2][$column] = $tempVal
		Next
		Return $returnMatrix
	EndIf
	Return -1
EndFunc   ;==>_Matrix_SwapRows
Func _Matrix_SwapColumns($aMatrix, $mColumn1, $mColumn2)
	If ($mColumn1 < UBound($aMatrix, 2)) And ($mColumn2 < UBound($aMatrix, 2)) Then
		Local $returnMatrix = $aMatrix
		Local $tempVal = 0
		For $row = 0 To UBound($aMatrix) - 1 Step 1
			$tempVal = $returnMatrix[$row][$mColumn1]
			$returnMatrix[$row][$mColumn1] = $returnMatrix[$row][$mColumn2]
			$returnMatrix[$row][$mColumn2] = $tempVal
		Next
		Return $returnMatrix
	EndIf
	Return -1
EndFunc   ;==>_Matrix_SwapColumns
Func _Matrix_TransposeMatrix($aMatrix)
	Local $returnMatrix[UBound($aMatrix, 2)][UBound($aMatrix)]
	For $row = 0 To UBound($aMatrix) - 1 Step 1
		For $column = 0 To UBound($aMatrix, 2) - 1 Step 1
			$returnMatrix[$column][$row] = $aMatrix[$row][$column]
		Next
	Next
	Return $returnMatrix
EndFunc   ;==>_Matrix_TransposeMatrix