

So, I've managed to trim down the number of errors that this gives me, but it
looks like there are a few things that need to be ironed out.
stdafx.h is just (commented out what looked to me like Windows specific stuff):
// stdafx.h : include file for standard system include files,
// or project specific include files that are used frequently, but
// are changed infrequently
//
#pragma once
//#include "targetver.h"
#include <stdio.h>
//#include <tchar.h>
// TODO: reference additional headers your program requires here

tried to compile:
oem@oemInspironN5110 ~/Documents/POVRay3.8/ThirdParty/jr/SVD/SVD $ c++
SVD.cpp std=c++11
std::cout << "Enter size of matrix N = (50x50 max): "; std::cin > >
matrix_size;
^
std::vector<std::vector<_RealType> >&, std::vector<std::vector<_RealType> >&,
std::vector<std::vector<_RealType> >&) [with Arg =
boost::multiprecision::number<boost::multiprecision::backends::cpp_bin_float<4096u,
(boost::multiprecision::backends::digit_base_type)2u, void, short int, 16382,
SVD.cpp:358:22: required from here
declarations were found by argumentdependent lookup at the point of
instantiation [fpermissive]
matrix_transpose(matrix, matrix_t);
^
matrix_transpose(std::vector<std::vector<_RealType> >,
unit
void matrix_transpose(std::vector<std::vector<Arg> > matrix1,
^
declarations were found by argumentdependent lookup at the point of
instantiation [fpermissive]
matrix_by_matrix(matrix, matrix_t, matrix_product1);
^
matrix_by_matrix(std::vector<std::vector<_RealType> >,
declared here, later in the translation unit
void matrix_by_matrix(std::vector<std::vector<Arg> > matrix1,
^
declarations were found by argumentdependent lookup at the point of
instantiation [fpermissive]
matrix_by_matrix(matrix_t, matrix, matrix_product2);
^
matrix_by_matrix(std::vector<std::vector<_RealType> >,
declared here, later in the translation unit
void matrix_by_matrix(std::vector<std::vector<Arg> > matrix1,
^
declarations were found by argumentdependent lookup at the point of
instantiation [fpermissive]
compute_evd(matrix_product2, eigenvalues, v_1, 0);
^
compute_evd(std::vector<std::vector<_RealType> >, std::vector<_RealType>&,
translation unit
void compute_evd(std::vector<std::vector<Arg> > matrix,
^
declarations were found by argumentdependent lookup at the point of
instantiation [fpermissive]
matrix_transpose(v_1, v);
^
matrix_transpose(std::vector<std::vector<_RealType> >,
unit
void matrix_transpose(std::vector<std::vector<Arg> > matrix1,
^
scope, and no declarations were found by argumentdependent lookup at the point
of instantiation [fpermissive]
get_inverse_diagonal_matrix(s, s_inverse);
^
get_inverse_diagonal_matrix(std::vector<std::vector<_RealType> >,
unit
void get_inverse_diagonal_matrix(std::vector<std::vector<Arg> > matrix,
^
declarations were found by argumentdependent lookup at the point of
instantiation [fpermissive]
matrix_by_matrix(matrix, v, av_matrix);
^
matrix_by_matrix(std::vector<std::vector<_RealType> >,
declared here, later in the translation unit
void matrix_by_matrix(std::vector<std::vector<Arg> > matrix1,
^
declarations were found by argumentdependent lookup at the point of
instantiation [fpermissive]
matrix_by_matrix(av_matrix, s_inverse, u);
^
matrix_by_matrix(std::vector<std::vector<_RealType> >,
declared here, later in the translation unit
void matrix_by_matrix(std::vector<std::vector<Arg> > matrix1,
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