diff --git a/fractions.hpp b/fractions.hpp
index 96a16e1..94fd998 100644
--- a/fractions.hpp
+++ b/fractions.hpp
@@ -4,9 +4,9 @@
 
 class fraction {
 private:
-  signed long long n = 0;
-  signed long long d = 1;
-  signed long long gcd(signed long long a, signed long long b) const {
+  uint64_t n = 0;
+  uint64_t d = 1;
+  uint64_t gcd(uint64_t a, uint64_t b) const {
     if (b == 0) {
       return a;
     }
@@ -37,19 +37,19 @@ public:
   // Constructors
   fraction() {}
   fraction(const fraction &q) {
-    signed long long hcf = gcd(q.n, q.d);
+    uint64_t hcf = gcd(q.n, q.d);
     n = q.n / hcf;
     d = q.d / hcf;
   }
-  fraction(signed long long a, signed long long b) {
-    signed long long hcf = gcd(a, b);
+  fraction(uint64_t a, uint64_t b) {
+    uint64_t hcf = gcd(a, b);
     n = a / hcf;
     d = b / hcf;
   }
   fraction(int a, int b) {
-    signed long long hcf = gcd(a, b);
-    n = (signed long long)a / hcf;
-    d = (signed long long)b / hcf;
+    uint64_t hcf = gcd(a, b);
+    n = (uint64_t)a / hcf;
+    d = (uint64_t)b / hcf;
   }
   fraction(int a) {
     fraction q(a, 1);
@@ -58,11 +58,11 @@ public:
   }
   fraction(double dec) {
     int precision = get_precision(dec);
-    signed long long denominator = 1;
+    uint64_t denominator = 1;
     for (int i = 0; i < precision; i++) {
       denominator *= 10;
     }
-    signed long long numerator = dec * denominator;
+    uint64_t numerator = dec * denominator;
     fraction q(numerator, denominator);
     n = q.n;
     d = q.d;
@@ -70,34 +70,34 @@ public:
   ~fraction() {}
   // Member functions
   int get_sign() const { return (!(n >= 0) != !(d >= 0)) ? -1 : 1; }
-  signed long long get_n() const { return this->n; }
-  signed long long get_d() const { return this->d; }
+  uint64_t get_n() const { return this->n; }
+  uint64_t get_d() const { return this->d; }
   double to_double() const {
     double dec = (double)n / (double)d;
     return dec;
   }
   // Operators
   fraction operator+(const fraction &that) const {
-    signed long long numerator = this->n * that.d + that.n * this->d;
-    signed long long denominator = this->d * that.d;
+    uint64_t numerator = this->n * that.d + that.n * this->d;
+    uint64_t denominator = this->d * that.d;
     fraction q(numerator, denominator);
     return q;
   }
   fraction operator-(const fraction &that) const {
-    signed long long numerator = this->n * that.d - that.n * this->d;
-    signed long long denominator = this->d * that.d;
+    uint64_t numerator = this->n * that.d - that.n * this->d;
+    uint64_t denominator = this->d * that.d;
     fraction q(numerator, denominator);
     return q;
   }
   fraction operator*(const fraction &that) const {
-    signed long long numerator = this->n * that.n;
-    signed long long denominator = this->d * that.d;
+    uint64_t numerator = this->n * that.n;
+    uint64_t denominator = this->d * that.d;
     fraction q(numerator, denominator);
     return q;
   }
   fraction operator*(const int i) const {
-    signed long long numerator = this->n * i;
-    signed long long denominator = this->d;
+    uint64_t numerator = this->n * i;
+    uint64_t denominator = this->d;
     fraction q(numerator, denominator);
     return q;
   }
@@ -107,8 +107,8 @@ public:
     return a * b;
   }
   friend std::ostream &operator<<(std::ostream &os, const fraction &q) {
-    signed long long num = q.n;
-    signed long long den = q.d;
+    uint64_t num = q.n;
+    uint64_t den = q.d;
     std::string s = "";
     if (q.n < 0) {
       s = "-";
@@ -135,8 +135,8 @@ public:
     this->d = q.d;
   }
   void operator=(const int i) {
-    this->n = (signed long long)i;
-    this->d = (signed long long)1;
+    this->n = (uint64_t)i;
+    this->d = (uint64_t)1;
   }
   void operator=(const double dec) {
     const fraction q(dec);
@@ -144,7 +144,7 @@ public:
     this->d = q.d;
   }
   bool operator>(const fraction &q) const {
-    signed long long hcf = gcd(d, q.d);
+    uint64_t hcf = gcd(d, q.d);
     fraction a(*this * hcf);
     fraction b(q * hcf);
     return (a.n > b.n);
diff --git a/main.cpp b/main.cpp
index e147fa7..67a57cb 100644
--- a/main.cpp
+++ b/main.cpp
@@ -140,7 +140,7 @@ void vector_main() {
   std::cout << v * w << std::endl;
   std::cout << "w * i:" << std::endl;
   std::cout << w * i << std::endl;
-  for (long long j = 0; j < v.get_dimention(); j++) {
+  for (uint64_t j = 0; j < v.get_dimention(); j++) {
 	  std::cout << "Element " << j << " of v:" << std::endl;
     	  std::cout << v[j] << std::endl;
   }
@@ -149,7 +149,7 @@ void vector_main() {
   k = w;
   std::cout << "Assignment of w to k" << std::endl << k << std::endl;
   std::cout << "Manually set elements of k to elements of v" << std::endl;
-  for (long long j = 0; j < v.get_dimention(); j++)
+  for (uint64_t j = 0; j < v.get_dimention(); j++)
     k[j] = v[j];
   std::cout << k << std::endl;
 }
diff --git a/matrix.hpp b/matrix.hpp
index 687d95a..b8eb88c 100644
--- a/matrix.hpp
+++ b/matrix.hpp
@@ -5,18 +5,18 @@
 #include <string>
 class matrix {
 private:
-  long long num_entries;
-  long long entry_dimension;
+  uint64_t num_entries;
+  uint64_t entry_dimension;
   vector *entries;
   bool err;
 
 public:
-  matrix(const long long num_entries, const long long entry_dimension) {
+  matrix(const uint64_t num_entries, const uint64_t entry_dimension) {
     this->num_entries = entry_dimension;
     this->entry_dimension = num_entries;
     this->err = false;
     this->entries = (vector *)malloc(sizeof(vector) * this->num_entries);
-    for (long long i = 0; i < entry_dimension; i++) {
+    for (uint64_t i = 0; i < entry_dimension; i++) {
       this->entries[i] = vector(this->entry_dimension);
     }
   }
@@ -25,7 +25,7 @@ public:
     this->entry_dimension = m.entry_dimension;
     this->err = m.err;
     this->entries = (vector *)malloc(sizeof(vector) * m.num_entries);
-    for (long long i = 0; i < m.num_entries; i++) {
+    for (uint64_t i = 0; i < m.num_entries; i++) {
       this->entries[i] = m[i];
     }
   }
@@ -36,27 +36,27 @@ public:
     this->entries = NULL;
     this->err = true;
   }
-  const long long get_num_entries() const { return this->num_entries; }
-  const long long get_entry_dimension() const { return this->entry_dimension; }
+  const uint64_t get_num_entries() const { return this->num_entries; }
+  const uint64_t get_entry_dimension() const { return this->entry_dimension; }
   const cnumber determinant() const {
     cnumber dsum(1, 0);
     cnumber osum(1, 0);
     vector diag = this->get_diagonal();
     vector odiag = this->get_off_diagonal();
-    for (long long i = 0; i < diag.get_dimention(); i++) {
+    for (uint64_t i = 0; i < diag.get_dimention(); i++) {
       dsum = dsum * diag[i];
       osum = osum * odiag[i];
     }
     return dsum - osum;
   }
   const vector get_diagonal() const {
-    long long diag_len = this->entry_dimension;
+    uint64_t diag_len = this->entry_dimension;
     if (this->num_entries < diag_len) {
       diag_len = this->num_entries;
     }
     vector v(diag_len);
-    for (long long i = 0; i < this->num_entries; i++) {
-      for (long long j = 0; j < this->entry_dimension; j++) {
+    for (uint64_t i = 0; i < this->num_entries; i++) {
+      for (uint64_t j = 0; j < this->entry_dimension; j++) {
         if (i == j) {
           v[i] = this->entries[i][j];
         }
@@ -65,22 +65,33 @@ public:
     return v;
   }
   const vector get_off_diagonal() const {
-    return this->rotate_by_one_pi().get_diagonal();
+    return this->rotate().get_diagonal();
   }
-  const vector get_entry(long long index) const { return this->entries[index]; }
 
-  const vector get_row(long long index) const {
+  const matrix get_echelon() const {
+    matrix m = *this;
+    if (!m.is_invertible()) {
+      m.err = true;
+    } else {
+      for (uint64_t i = 0; i < m.get_num_entries(); i++) {
+      }
+    }
+    return m;
+  }
+  const vector get_entry(uint64_t index) const { return this->entries[index]; }
+
+  const vector get_row(uint64_t index) const {
     vector v(this->entry_dimension);
-    for (long long j = 0; j < this->entry_dimension; j++) {
+    for (uint64_t j = 0; j < this->entry_dimension; j++) {
       v[j] = this->entries[j][index];
     }
     return v;
   }
 
-  const matrix rotate_by_one_pi() const {
+  const matrix rotate() const {
     matrix m = this->transpose();
     matrix n = matrix(m.entry_dimension, m.num_entries);
-    for (long long i = 0; i < m.entry_dimension; i++) {
+    for (uint64_t i = 0; i < m.entry_dimension; i++) {
       int index = m.num_entries - i - 1;
       n[i] = m[index];
     }
@@ -88,8 +99,8 @@ public:
   }
   const matrix transpose() const {
     matrix n = matrix(this->entry_dimension, this->num_entries);
-    for (long long i = 0; i < this->num_entries; i++) {
-      for (long long j = 0; j < this->entry_dimension; j++) {
+    for (uint64_t i = 0; i < this->num_entries; i++) {
+      for (uint64_t j = 0; j < this->entry_dimension; j++) {
         n[j][i] = this->entries[i][j];
       }
     }
@@ -98,8 +109,8 @@ public:
   }
   const matrix conjugate() const {
     matrix n = matrix(this->num_entries, this->entry_dimension);
-    for (long long i = 0; i < this->num_entries; i++) {
-      for (long long j = 0; j < this->entry_dimension; j++) {
+    for (uint64_t i = 0; i < this->num_entries; i++) {
+      for (uint64_t j = 0; j < this->entry_dimension; j++) {
         n[i][j] = this->entries[i][j].conjugate();
       }
     }
@@ -111,8 +122,8 @@ public:
   }
   const matrix I() const {
     matrix m = matrix(this->num_entries, this->entry_dimension);
-    for (long long i = 0; i < this->num_entries; i++) {
-      for (long long j = 0; j < this->entry_dimension; j++) {
+    for (uint64_t i = 0; i < this->num_entries; i++) {
+      for (uint64_t j = 0; j < this->entry_dimension; j++) {
         if (i == j) {
           m[i][j] = cnumber(1, 0);
         } else {
@@ -126,8 +137,8 @@ public:
     bool result = true;
     if (this->num_entries != this->entry_dimension)
       return !result;
-    for (long long i = 0; i < this->num_entries; i++) {
-      for (long long j = 0; j < this->num_entries; j++) {
+    for (uint64_t i = 0; i < this->num_entries; i++) {
+      for (uint64_t j = 0; j < this->num_entries; j++) {
         if (i != j && this->entries[i][j] != 0)
           return !result;
       }
@@ -155,8 +166,8 @@ public:
   friend std::ostream &operator<<(std::ostream &os, const matrix &m) {
     char last = '\0';
     int longest = 0;
-    for (long long i = 0; i < m.num_entries; i++) {
-      for (long long j = 0; j < m.entry_dimension; j++) {
+    for (uint64_t i = 0; i < m.num_entries; i++) {
+      for (uint64_t j = 0; j < m.entry_dimension; j++) {
         std::ostringstream oss;
         oss << m.entries[i][j];
         std::string s = oss.str();
@@ -164,17 +175,17 @@ public:
           longest = s.length();
       }
     }
-    for (long long i = 0; i < m.num_entries; i++) {
-      for (long long j = 0; j < m.entry_dimension; j++) {
+    for (uint64_t i = 0; i < m.num_entries; i++) {
+      for (uint64_t j = 0; j < m.entry_dimension; j++) {
         std::ostringstream iss;
         iss << m.entries[i][j];
         std::string s = iss.str();
-        int padding = longest - s.length() +1;
+        int padding = longest - s.length() + 1;
         std::string symbols[3];
         symbols[0] = "|";
         std::ostringstream oss;
-        oss << m.entries[i][j] ;
-	oss << std::setw(padding) << "|";
+        oss << m.entries[i][j];
+        oss << std::setw(padding) << "|";
         symbols[1] = oss.str();
         symbols[2] = "|";
         for (int i = 0; i < 3; i++) {
@@ -193,8 +204,8 @@ public:
   }
   const bool operator==(const matrix &m) const {
     bool equal = true;
-    for (long long i = 0; i < this->num_entries; i++) {
-      for (long long j = 0; j < this->entry_dimension; j++) {
+    for (uint64_t i = 0; i < this->num_entries; i++) {
+      for (uint64_t j = 0; j < this->entry_dimension; j++) {
         if (this->entries[i][j] != m[i][j]) {
           equal = false;
         }
@@ -202,13 +213,13 @@ public:
     }
     return equal;
   }
-  vector &operator[](const long long index) { return this->entries[index]; }
-  const vector operator[](const long long index) const {
+  vector &operator[](const uint64_t index) { return this->entries[index]; }
+  const vector operator[](const uint64_t index) const {
     return this->entries[index];
   }
   const matrix operator*(const cnumber z) const {
     matrix n(this->num_entries, this->entry_dimension);
-    for (long long i = 0; i < this->num_entries; i++) {
+    for (uint64_t i = 0; i < this->num_entries; i++) {
       n[i] = this->entries[i] * z;
     }
 
@@ -217,8 +228,8 @@ public:
 
   const matrix operator*(vector &v) const {
     matrix res(this->get_num_entries(), this->get_entry_dimension());
-    for (long long i = 0; i < this->get_num_entries(); i++) {
-      for (long long j = 0; j < this->get_entry_dimension(); j++) {
+    for (uint64_t i = 0; i < this->get_num_entries(); i++) {
+      for (uint64_t j = 0; j < this->get_entry_dimension(); j++) {
         res[i][j] = (this->get_entry(i)[j] * v.get_entry(i));
       }
     }
@@ -232,8 +243,8 @@ public:
       n.err = true;
       return n;
     }
-    for (long long i = 0; i < this->entry_dimension; i++) {
-      for (long long j = 0; j < this->entry_dimension; j++) {
+    for (uint64_t i = 0; i < this->entry_dimension; i++) {
+      for (uint64_t j = 0; j < this->entry_dimension; j++) {
         n[i][j] = this->get_entry(i) * m.get_row(j);
       }
     }
@@ -243,7 +254,7 @@ public:
 
   const matrix operator+(const matrix &m) const {
     matrix n(this->num_entries, this->entry_dimension);
-    for (long long i = 0; i < this->num_entries; i++) {
+    for (uint64_t i = 0; i < this->num_entries; i++) {
       n[i] = this->entries[i] + m[i];
     }
 
@@ -251,7 +262,7 @@ public:
   }
   const matrix operator-(const matrix &m) const {
     matrix n(this->num_entries, this->entry_dimension);
-    for (long long i = 0; i < this->num_entries; i++) {
+    for (uint64_t i = 0; i < this->num_entries; i++) {
       n[i] = this->entries[i] - m[i];
     }
 
@@ -263,7 +274,7 @@ public:
     this->err = m.err;
     free(this->entries);
     this->entries = (vector *)malloc(sizeof(vector) * m.num_entries);
-    for (long long i = 0; i < m.num_entries; i++)
+    for (uint64_t i = 0; i < m.num_entries; i++)
       this->entries[i] = m[i];
   }
 };
diff --git a/vector.cpp b/vector.cpp
index 26ca99e..3d319be 100644
--- a/vector.cpp
+++ b/vector.cpp
@@ -2,9 +2,9 @@
 #include "matrix.hpp"
 const vector vector::operator*(const matrix &m) const {
   vector res(m.get_num_entries());
-  for (long long i = 0; i < this->get_dimention(); i++) {
+  for (uint64_t i = 0; i < this->get_dimention(); i++) {
     cnumber sum = 0;
-    for (long long j = 0; j < this->get_dimention(); j++) {
+    for (uint64_t j = 0; j < this->get_dimention(); j++) {
       sum = sum + (m.get_entry(j)[i] * this->entries[j]);
     }
     res[i] = sum;
diff --git a/vector.hpp b/vector.hpp
index 5b32640..d4c4e5a 100644
--- a/vector.hpp
+++ b/vector.hpp
@@ -5,19 +5,19 @@
 class matrix;
 class vector {
 private:
-  long long dimention = 0;
+  uint64_t dimention = 0;
   cnumber *entries = NULL;
   bool err = true;
 
 public:
   bool is_error() { return this->err; }
   vector(){};
-  vector(const long long dimention) {
+  vector(const uint64_t dimention) {
     this->err = false;
     this->dimention = dimention;
     free(this->entries);
     this->entries = (cnumber *)malloc(sizeof(cnumber) * dimention);
-    for (long long i = 0; i < dimention; i++) {
+    for (uint64_t i = 0; i < dimention; i++) {
       this->set_entry(i, cnumber(0, 0));
     }
   }
@@ -26,7 +26,7 @@ public:
     this->dimention = v.get_dimention();
     free(this->entries);
     this->entries = (cnumber *)malloc(sizeof(cnumber) * v.get_dimention());
-    for (long long i = 0; i < v.get_dimention(); i++) {
+    for (uint64_t i = 0; i < v.get_dimention(); i++) {
       this->set_entry(i, v.get_entry(i));
     }
   }
@@ -36,38 +36,38 @@ public:
     // this->entries = NULL;
     this->err = true;
   }
-  long long get_dimention() const { return this->dimention; }
+  uint64_t get_dimention() const { return this->dimention; }
   const cnumber *get_entries() const { return this->entries; }
-  cnumber get_entry(const long long index) const {
+  cnumber get_entry(const uint64_t index) const {
     if (index < this->get_dimention()) {
       return this->entries[index];
     }
     return cnumber(0, 0);
   }
-  void set_entry(const long long index, const cnumber z) {
+  void set_entry(const uint64_t index, const cnumber z) {
     if (index < this->get_dimention()) {
       this->entries[index] = z;
     }
   }
 
-  const cnumber operator[](const long long index) const {
+  const cnumber operator[](const uint64_t index) const {
     return this->get_entry(index);
   }
 
   // FIXME: Figure out how to make sure you do not try to access something
   // outside of the index
-  cnumber &operator[](const long long index) { return this->entries[index]; }
+  cnumber &operator[](const uint64_t index) { return this->entries[index]; }
 
   friend std::ostream &operator<<(std::ostream &os, const vector &v) {
     int longest = 0;
-    for (long long i = 0; i < v.get_dimention(); i++) {
+    for (uint64_t i = 0; i < v.get_dimention(); i++) {
 	    std::ostringstream oss;
       oss << v[i];
       std::string s = oss.str();
       if (longest < s.length())
 	      longest = s.length();
     }
-    for (long long i = 0; i < v.get_dimention(); i++) {
+    for (uint64_t i = 0; i < v.get_dimention(); i++) {
 	    std::ostringstream oss;
       oss << v[i];
       std::string s = oss.str();
@@ -82,7 +82,7 @@ public:
     this->dimention = v.get_dimention();
     free(this->entries);
     this->entries = (cnumber *)malloc(sizeof(cnumber) * dimention);
-    for (long long i = 0; i < v.get_dimention(); i++) {
+    for (uint64_t i = 0; i < v.get_dimention(); i++) {
       this->set_entry(i, v.get_entry(i));
     }
     this->err = false;
@@ -92,7 +92,7 @@ public:
       return vector(0);
     }
     vector sum = vector(v.get_dimention());
-    for (long long i = 0; i < v.get_dimention(); i++) {
+    for (uint64_t i = 0; i < v.get_dimention(); i++) {
       sum[i] = this->get_entry(i) + v[i];
     }
     return sum;
@@ -103,7 +103,7 @@ public:
       return vector(0);
     }
     vector sum = vector(v.get_dimention());
-    for (long long i = 0; i < v.get_dimention(); i++) {
+    for (uint64_t i = 0; i < v.get_dimention(); i++) {
       sum[i] = this->entries[i] - v[i];
     }
     return sum;
@@ -111,14 +111,14 @@ public:
   const vector operator*(const matrix &m) const;
   const vector operator*(const cnumber scalar) const {
     vector product = vector(this->get_dimention());
-    for (long long i = 0; i < this->get_dimention(); i++) {
+    for (uint64_t i = 0; i < this->get_dimention(); i++) {
       product[i] = this->entries[i] * scalar;
     }
     return product;
   }
   const cnumber operator*(const vector &v) const {
     cnumber res(0, 0);
-    for (long long i = 0; i < this->get_dimention(); i++) {
+    for (uint64_t i = 0; i < this->get_dimention(); i++) {
       res = res + this->get_entry(i) * v.get_entry(i);
     }
     return res;