diff --git a/matrix.cpp b/matrix.cpp
index 897b9a9..279f52a 100644
--- a/matrix.cpp
+++ b/matrix.cpp
@@ -4,25 +4,33 @@
 
 int main() {
   vector a = vector(3);
-  a[0] = cnumber(1, 0);
-  a[1] = cnumber(0, 0);
-  a[2] = cnumber(0, 0);
+  a[0] = cnumber(7, 0);
+  a[1] = cnumber(5, 0);
+  a[2] = cnumber(0, 1);
 
   vector b = vector(3);
   b[0] = cnumber(0, 0);
-  b[1] = cnumber(1, 0);
+  b[1] = cnumber(2, 0);
   b[2] = cnumber(0, 0);
 
   vector c = vector(3);
-  c[0] = cnumber(0, 0);
+  c[0] = cnumber(0, -1);
   c[1] = cnumber(0, 0);
-  c[2] = cnumber(0, -1);
+  c[2] = cnumber(4, 0);
 
   matrix m = matrix(3, 3);
   m[0] = a;
   m[1] = b;
   m[2] = c;
 
+  cout << "The matrix m:" << endl;
   cout << m << endl;
+  cout << "The matrix m's transpose:" << endl;
+  cout << m.transpose() << endl;
+  if  (!m.is_hermitian()) {
+    cout << "The matrix m is not hermitian, here is the hermitian conjugate:"
+         << endl;
+    cout << m.hermitian_conjugate() << endl;
+  }
   return 0;
 }
diff --git a/matrix.hpp b/matrix.hpp
index bae6c0c..cc4ea15 100644
--- a/matrix.hpp
+++ b/matrix.hpp
@@ -5,33 +5,85 @@
 using namespace std;
 class matrix {
 private:
-  long long num_rows;
   long long num_cols;
-  vector *rows;
+  long long num_rows;
+  vector *cols;
 
 public:
-  matrix(const long long num_rows, const long long num_cols) {
-    this->num_rows = num_rows;
-    this->num_cols = num_cols;
-    this->rows = (vector *)calloc(sizeof(vector), num_rows);
+  matrix(const long long num_cols, const long long num_rows) {
+    this->num_cols = num_rows;
+    this->num_rows = num_cols;
+    this->cols = (vector *)calloc(sizeof(vector), num_rows);
     for (long long i = 0; i < num_rows; i++) {
-      this->rows[i] = vector(num_cols);
+      this->cols[i] = vector(num_cols);
     }
   }
   ~matrix() {
-    this->num_rows = 0;
     this->num_cols = 0;
-    free(this->rows);
-    this->rows = NULL;
+    this->num_rows = 0;
+    free(this->cols);
+    this->cols = NULL;
+  }
+  const vector get_diagonal() const {
+    long long diag_len = this->num_rows;
+    if (this->num_cols < diag_len) {
+      diag_len = this->num_cols;
+    }
+    vector v(diag_len);
+    for (long long i = 0; i < this->num_cols; i++) {
+      for (long long j = 0; j < this->num_rows; j++) {
+        if (i == j) {
+          v[i] = this->cols[i][j];
+        }
+      }
+    }
+    return v;
+  }
+  const matrix transpose() const {
+    matrix n(this->num_rows, this->num_cols);
+    for (long long i = 0; i < this->num_cols; i++) {
+      for (long long j = 0; j < this->num_rows; j++) {
+        n[j][i] = this->cols[i][j];
+      }
+    }
+
+    return n;
+  }
+  const matrix conjugate() const {
+    matrix n(this->num_cols, this->num_rows);
+    for (long long i = 0; i < this->num_cols; i++) {
+      for (long long j = 0; j < this->num_rows; j++) {
+        n[i][j] = this->cols[i][j].conjugate();
+      }
+    }
+
+    return n;
+  }
+  const matrix hermitian_conjugate() const {
+    return this->transpose().conjugate();
+  }
+  const bool is_hermitian() const {
+    if (this->num_rows != this->num_cols)
+	    return false;
+    matrix m = this->hermitian_conjugate();
+    bool equal = true;
+    for (long long i = 0; i < m.num_cols; i++) {
+      for (long long j = 0; j < m.num_rows; j++) {
+        if (m[i][j] != this->cols[i][j]) {
+          equal = false;
+        }
+      }
+    }
+    return equal;
   }
   friend ostream &operator<<(ostream &os, const matrix &m) {
     char last = '\0';
-    for (long long i = 0; i < m.num_rows; i++) {
-      for (long long j = 0; j < m.num_cols; j++) {
+    for (long long i = 0; i < m.num_cols; i++) {
+      for (long long j = 0; j < m.num_rows; j++) {
         string symbols[3];
         symbols[0] = "|";
         ostringstream oss;
-        oss << " " << m.rows[i][j] << " ";
+        oss << " " << m.cols[i][j] << " ";
         symbols[1] = oss.str();
         symbols[2] = "|";
         for (int i = 0; i < 3; i++) {
@@ -43,16 +95,51 @@ public:
           last = symbols[i][len];
         }
       }
-      if (i != m.num_rows - 1)
+      if (i != m.num_cols - 1)
         os << endl << "|";
     }
     return os;
   }
+  const bool operator==(const matrix &m) const {
+    bool equal = true;
+    for (long long i = 0; i < this->num_cols; i++) {
+      for (long long j = 0; j < this->num_rows; j++) {
+        if (this->cols[i][j] != m[i][j]) {
+          equal = false;
+        }
+      }
+    }
+    return equal;
+  }
   const vector operator[](const long long index) const {
-    return this->rows[index];
+    return this->cols[index];
   }
+  const matrix operator*(const cnumber z) const {
+    matrix n(this->num_cols, this->num_rows);
+    for (long long i = 0; i < this->num_cols; i++) {
+      n[i] = this->cols[i] * z;
+    }
 
+    return n;
+  }
+
+  const matrix operator+(const matrix &m) const {
+    matrix n(this->num_cols, this->num_rows);
+    for (long long i = 0; i < this->num_cols; i++) {
+      n[i] = this->cols[i] + m[i];
+    }
+
+    return n;
+  }
+  const matrix operator-(const matrix &m) const {
+    matrix n(this->num_cols, this->num_rows);
+    for (long long i = 0; i < this->num_cols; i++) {
+      n[i] = this->cols[i] - m[i];
+    }
+
+    return n;
+  }
   // FIXME: Figure out how to make sure you do not try to access something
   // outside of the index
-  vector &operator[](const long long index) { return this->rows[index]; }
+  vector &operator[](const long long index) { return this->cols[index]; }
 };
diff --git a/test b/test
deleted file mode 100755
index 47884ca..0000000
Binary files a/test and /dev/null differ