Call non-member function from inside class, but the nonmember function takes class as input (C++)

As the title suggests, I am wondering if I can call a non-member function (which is contained in the class header file) from inside the class, with the caveat that the nonmember function is using the class itself ? Normally I could just put the nonmember function above the class declaration, but that means I cannot pass it the class as input because it is not identified by then.

For reference this is what a slimmed down version of my "Matrix" class looks like, with the nonmember function "LUDecomposition", which I am trying to call from the "Determinant" member class:

#pragma once #include <vector> #include <tuple> enum MatrixType { Identity, Zeros, Ones }; class Matrix { private: int col, row; typedef std::vector<double> Row; std::vector<Row> data; public: Matrix(int columns, int rows): row(rows), col(columns), data(columns, std::vector<double>(rows)) { } Matrix(int columns, int rows, MatrixType matrixType) : row(rows), col(columns), data(columns, std::vector<double>(rows)) { switch (matrixType) { case Identity: this->MakeIdentity(); break; case Zeros: this->Fill(0); break; case Ones: this->Fill(1); break; default: break; } } Row& operator[](int i) { return data[i]; } std::tuple<int,int> Size() const { return std::make_tuple(col, row); } double Determinant() const { if (col != row) throw std::exception("Matrix must be square"); Matrix tempMatrix = *this; std::tuple<Matrix, Matrix> LU = LUDecomposition(tempMatrix); } }; std::tuple<Matrix, Matrix> LUDecomposition(Matrix& matrix) //This function decomposes input square matrix A into lower triangular matrix L and upper triangular matrix U such that A=LU (Doolittle) { std::tuple<int, int> size = matrix.Size(); int col = std::get<0>(size); int row = std::get<1>(size); Matrix lower(col, row); Matrix upper(col, row); for (int i = 0; i < col; i++) { for (int k = i; k < col; k++) { int sum = 0; for (int j = 0; j < i; j++) { sum += lower[j][i] * upper[k][j]; } upper[k][i] = matrix[k][i] - sum; } for (int k = i; k < col; k++) { if (i == k) lower[i][i] = 1; else { int sum = 0; for (int j = 0; j < i; j++) { sum += lower[j][k] * upper[i][j]; } lower[i][k] = (matrix[i][k] - sum) / upper[i][i]; } } } return std::make_tuple(lower, upper); } 

Is there any way at all to call this function from inside the class ? I don't mind if it remains a nonmember function, or is moved somewhere, just trying to find a way to do this.