diff --git a/ChangeLog b/ChangeLog
index 4f78bb9..e69de29 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,52 +0,0 @@
-2016-08-19 14:52  
-
-	* COPYING, INSTALL, ax_cxx_compile_stdcxx_11.m4,
-	  ax_init_standard_project.m4, bootstrap.sh, makefile_test.inc.am,
-	  src/matrix.hxx, test/basic.cxx: more operators more tests
-
-2016-08-18 22:03  
-
-	* COPYING, ChangeLog, INSTALL, src/matrix.hxx: more operators
-
-2016-08-17 07:26  
-
-	* configure.ac: only requires c++11
-
-2016-08-16 14:41  
-
-	* COPYING, INSTALL, ax_init_standard_project.m4, configure.ac,
-	  src/matrix.hxx, test/basic.cxx: remove redundancy, collect common
-	  functionality in base class
-
-2016-08-08 20:03  
-
-	* src/matrix.hxx, test/basic.cxx: more operator, more checks passed
-
-2016-08-03 18:43  
-
-	* configure.ac, test/makefile.am: all tests passed
-
-2016-08-03 18:39  
-
-	* COPYING, ChangeLog, INSTALL, ax_cxx_compile_stdcxx_11.m4,
-	  ax_init_standard_project.m4, configure.ac, examples/makefile.am,
-	  examples/matrix-sample.cxx, src/makefile.am, src/matrix.hxx,
-	  test/basic.cxx, test/makefile.am: first approach including first
-	  tests
-
-2016-07-30 08:50  
-
-	* ., AUTHORS, ChangeLog, NEWS, README, autogen.sh, ax_check_qt.m4,
-	  ax_cxx_compile_stdcxx_11.m4, ax_init_standard_project.m4,
-	  bootstrap.sh, build-in-docker.conf, build-in-docker.sh,
-	  build-resource-file.sh, configure.ac, debian,
-	  debian/changelog.in, debian/compat, debian/control.in,
-	  debian/docs, debian/libmatricxx-dev.install,
-	  debian/libmatricxx.install, debian/rules, doc, doc/doxyfile.in,
-	  doc/makefile.am, examples, examples/makefile.am,
-	  libmatricxx.desktop.in, libmatricxx.spec.in,
-	  mac-create-app-bundle.sh, makefile.am, resolve-debbuilddeps.sh,
-	  resolve-rpmbuilddeps.sh, sql-to-dot.sed, src,
-	  src/libmatricxx.pc.in, src/makefile.am, src/version.cxx,
-	  src/version.hxx, test, test/makefile.am: initial project
-
diff --git a/src/matrix.hxx b/src/matrix.hxx
index c331739..6fa2e34 100644
--- a/src/matrix.hxx
+++ b/src/matrix.hxx
@@ -177,26 +177,32 @@ template<typename TYPE, typename ARRAY=TYPE*> class MatrixBase {
     ///{
 
     TYPE det() {
-      // rule of sarrus
-      TYPE res(0);
-      assert(ROWS==COLUMNS); // not really necessary
-      // 1) terms to add
-      for (size_t i(0); i<COLUMNS; ++i) {
-        TYPE term(1);
-        for (size_t j(0); j<ROWS; ++j)
-          term *= at((i+j)%COLUMNS, j);
-        res += term;
-      }
-      // 2) terms to subtract
-      for (size_t i(0); i<COLUMNS; ++i) {
-        TYPE term(1);
-        for (size_t j(0); j<ROWS; ++j)
-          term *= at((i+j)%COLUMNS, ROWS-j-1);
-        res -= term;
-      }
+      TYPE res(gauss());
+      for (TYPE *p((TYPE*)(_c)+SIZE); --p>=(TYPE*)(_c); p-=COLUMNS) res *= *p;
       return res;
     }
 
+    TYPE gauss() {
+      /// calculate using gauss algorithmus
+      /// @see http://www.mathebibel.de/determinante-berechnen-nach-gauss
+      /// 1. normalize first line to first value
+      TYPE lambda(at(0, 0));
+      at(0, 0) = 1;
+      for (TYPE *p((TYPE*)(_c)+COLUMNS); p>(TYPE*)(_c)+1;) *--p/=lambda;
+      /// 2. nullify lower triangle
+      for (size_t column(0); column<COLUMNS-1; ++column) {
+        for (size_t row(column+1); row<ROWS; ++row) {
+          TYPE pivot(at(row, column));
+          if (pivot!=0) {
+            at(row, column) = 0;
+            for (size_t pos(column+1); pos<COLUMNS; ++pos)
+              at(row, pos) -= pivot*at(0, pos);
+          }
+        }
+      }
+      return lambda;
+    }
+
     ///}
     
     //................................................................methods
@@ -284,6 +290,42 @@ template<typename TYPE, size_t TROWS=0, size_t TCOLUMNS=0> class Matrix:
       return res;
     }
 
+    static Matrix i() {
+      Matrix res;
+      for (size_t row(0); row<TROWS&&row<TCOLUMNS; ++row) res(row, row) = 1;
+      return res;
+    }
+
+    Matrix& inv() {
+      /// calculate using gauss-jordan algorithmus
+      /// @see http://www.mathebibel.de/inverse-matrix-berechnen-nach-gauss-jordan
+      Matrix o(*this); // left side
+      *this = i(); // right side
+      /// 1. lower left part
+      for (size_t row(0); row<this->ROWS; ++row)
+        if (rows<this->COLUMNS) {
+          /// 2. normalize first line to first value
+          TYPE pivot(o(row, row));
+          if (pivot!=1) {
+            o(row, row) = 1;
+            for (size_t column(row+1); column<this->COLUMNS; ++column) o(row, column)/=pivot;
+            for (size_t column(row); column<this->COLUMNS; ++column) this->at(row, column)/=pivot;
+          }
+          /// 3. nullify lower triangle
+          for (size_t row(column+1); row<this->ROWS; ++row) {
+            TYPE pivot(o(row, column));
+            if (pivot!=0) {
+              o(row, column) = 0;
+              for (size_t pos(column+1); pos<this->COLUMNS; ++pos) o(row, pos) -= pivot*o(0, pos);
+              for (size_t pos(column); pos<this->COLUMNS; ++pos) this->at(row, pos) -= pivot*this->at(0, pos);
+            }
+          }
+        }
+      /// 4. nullify the upper triangle
+      
+      return *this;
+    }
+
     ///}
 };
 
@@ -306,6 +348,8 @@ template<typename TYPE> class Matrix<TYPE, 0, 0>: public MatrixBase<TYPE> {
     
     Matrix(size_t rows, size_t columns):
         Parent(rows, columns) {
+      assert(rows>0);
+      assert(columns>0);
       Parent::_c = new TYPE[rows*columns];
       memset(Parent::_c, 0, Parent::MEM_SIZE);
     }
@@ -347,14 +391,6 @@ template<typename TYPE> class Matrix<TYPE, 0, 0>: public MatrixBase<TYPE> {
       return Parent::operator=(o);
     }
 
-    Matrix t() const {
-      Matrix res(Parent::COLUMNS, Parent::ROWS);
-      for (size_t row(0); row<Parent::ROWS; ++row)
-        for (size_t column(0); column<Parent::COLUMNS; ++column)
-          res(column, row) = this->at(row, column);
-      return res;
-    }
-
     Matrix operator-() const {
       Matrix res(Parent::COLUMNS, Parent::ROWS);
       for (TYPE *to((TYPE*)(res._c)+Parent::SIZE); to>(TYPE*)(Parent::_c); --to)
@@ -374,16 +410,36 @@ template<typename TYPE> class Matrix<TYPE, 0, 0>: public MatrixBase<TYPE> {
 
     ///}
 
+    ///@name special operations
+    ///{
+    
+    Matrix t() const {
+      Matrix res(this->COLUMNS, this->ROWS);
+      for (size_t row(0); row<this->ROWS; ++row)
+        for (size_t column(0); column<this->COLUMNS; ++column)
+          res(column, row) = this->at(row, column);
+      return res;
+    }
+
+    Matrix i() const {
+      Matrix res(this->ROWS, this->COLUMNS);
+      for (size_t row(0); row<this->ROWS&&row<this->COLUMNS; ++row)
+        res(row, row) = 1;
+      return res;
+    }
+
+    ///}
+
     //................................................................methods
   protected:
 
     virtual void assert_check(const Matrix& o) const {
-      assert(o.ROWS==Parent::ROWS);
-      assert(o.COLUMNS==Parent::COLUMNS);
+      assert(o.ROWS==this->ROWS);
+      assert(o.COLUMNS==this->COLUMNS);
     }
 
     virtual bool check(const Matrix& o) const {
-      return o.ROWS==Parent::ROWS && o.COLUMNS==Parent::COLUMNS;
+      return o.ROWS==this->ROWS && o.COLUMNS==this->COLUMNS;
     }
 
     void copy_args(TYPE*) {}
diff --git a/test/basic.cxx b/test/basic.cxx
index a678871..3664281 100644
--- a/test/basic.cxx
+++ b/test/basic.cxx
@@ -169,6 +169,53 @@ class TemplateMatrixTest: public CppUnit::TestFixture {
                               3, 6);
       CPPUNIT_ASSERT_EQUAL(res, m.t());
     }
+    template<typename T>
+        void gauss() {
+      Matrix<T,3,3> m(2, -2, 4,
+                      -2, 1, -6,
+                      1, 0, -2);
+      const Matrix<T,3,3> res(1, -1, 2,
+                              0, -1, -2,
+                              0, 0, -6);
+      T lambda(m.gauss());
+      CPPUNIT_ASSERT_EQUAL(res, m);
+      CPPUNIT_ASSERT_EQUAL((T)2, lambda);
+    }
+    template<typename T>
+        void det() {
+      Matrix<T,3,3> m(2, -2, 4,
+                      -2, 1, -6,
+                      1, 0, -2);
+      CPPUNIT_ASSERT_EQUAL((T)12, m.det());
+    }
+    template<typename T>
+        void i() {
+      const Matrix<T,3,3> m1(1, 0, 0,
+                             0, 1, 0,
+                             0, 0, 1);
+      const Matrix<T,3,2> m2(1, 0,
+                             0, 1,
+                             0, 0);
+      const Matrix<T,2,3> m3(1, 0, 0,
+                             0, 1, 0);
+      CPPUNIT_ASSERT_EQUAL(m1, m1.i());
+      CPPUNIT_ASSERT_EQUAL(m2, m2.i());
+      CPPUNIT_ASSERT_EQUAL(m3, m3.i());
+    }
+    template<typename T>
+        void inv() {
+      Matrix<T,3,3> m(2, -1, 0,
+                      1, 2, -2,
+                      0, -1, 1);
+      const Matrix<T,3,3> res(0.5, 0, 0,
+                              -0.2, 0.4, 0,
+                              -1, 2, 5);
+      // const Matrix<T,3,3> res(0, 1, 2,
+      //                         -1, 2, 4,
+      //                         -1, 2, 5);
+      m.inv();
+      CPPUNIT_ASSERT_EQUAL(res, m);
+    }
     CPPUNIT_TEST_SUITE(TemplateMatrixTest);
     CPPUNIT_TEST(initFromArray1<int>);
     CPPUNIT_TEST(initFromArray1<long>);
@@ -236,6 +283,22 @@ class TemplateMatrixTest: public CppUnit::TestFixture {
     CPPUNIT_TEST(transpose<unsigned long>);
     CPPUNIT_TEST(transpose<float>);
     CPPUNIT_TEST(transpose<double>);
+    CPPUNIT_TEST(gauss<int>);
+    CPPUNIT_TEST(gauss<long>);
+    CPPUNIT_TEST(gauss<float>);
+    CPPUNIT_TEST(gauss<double>);
+    CPPUNIT_TEST(det<int>);
+    CPPUNIT_TEST(det<long>);
+    CPPUNIT_TEST(det<float>);
+    CPPUNIT_TEST(det<double>);
+    CPPUNIT_TEST(i<int>);
+    CPPUNIT_TEST(i<long>);
+    CPPUNIT_TEST(i<unsigned>);
+    CPPUNIT_TEST(i<unsigned long>);
+    CPPUNIT_TEST(i<float>);
+    CPPUNIT_TEST(i<double>);
+    CPPUNIT_TEST(inv<float>);
+    CPPUNIT_TEST(inv<double>);
     CPPUNIT_TEST_SUITE_END();
 };
 CPPUNIT_TEST_SUITE_REGISTRATION(TemplateMatrixTest);
@@ -400,6 +463,45 @@ class VariableMatrixTest: public CppUnit::TestFixture {
                           3, 6);
       CPPUNIT_ASSERT_EQUAL(res, m.t());
     }
+    template<typename T>
+        void gauss() {
+      Matrix<T> m(3, 3,
+                  2, -2, 4,
+                  -2, 1, -6,
+                  1, 0, -2);
+      const Matrix<T> res(3,3,
+                          1, -1, 2,
+                          0, -1, -2,
+                          0, 0, -6);
+      T lambda(m.gauss());
+      CPPUNIT_ASSERT_EQUAL(res, m);
+      CPPUNIT_ASSERT_EQUAL((T)2, lambda);
+    }
+    template<typename T>
+        void det() {
+      Matrix<T> m(3, 3,
+                  2, -2, 4,
+                  -2, 1, -6,
+                  1, 0, -2);
+      CPPUNIT_ASSERT_EQUAL((T)12, m.det());
+    }
+    template<typename T>
+        void i() {
+      const Matrix<T> m1(3, 3,
+                         1, 0, 0,
+                         0, 1, 0,
+                         0, 0, 1);
+      const Matrix<T> m2(3, 2,
+                         1, 0,
+                         0, 1,
+                         0, 0);
+      const Matrix<T> m3(2, 3,
+                         1, 0, 0,
+                         0, 1, 0);
+      CPPUNIT_ASSERT_EQUAL(m1, m1.i());
+      CPPUNIT_ASSERT_EQUAL(m2, m2.i());
+      CPPUNIT_ASSERT_EQUAL(m3, m3.i());
+    }
     CPPUNIT_TEST_SUITE(VariableMatrixTest);
     CPPUNIT_TEST(initFromArray1<int>);
     CPPUNIT_TEST(initFromArray1<long>);
@@ -467,6 +569,20 @@ class VariableMatrixTest: public CppUnit::TestFixture {
     CPPUNIT_TEST(transpose<unsigned long>);
     CPPUNIT_TEST(transpose<float>);
     CPPUNIT_TEST(transpose<double>);
+    CPPUNIT_TEST(gauss<int>);
+    CPPUNIT_TEST(gauss<long>);
+    CPPUNIT_TEST(gauss<float>);
+    CPPUNIT_TEST(gauss<double>);
+    CPPUNIT_TEST(det<int>);
+    CPPUNIT_TEST(det<long>);
+    CPPUNIT_TEST(det<float>);
+    CPPUNIT_TEST(det<double>);
+    CPPUNIT_TEST(i<int>);
+    CPPUNIT_TEST(i<long>);
+    CPPUNIT_TEST(i<unsigned>);
+    CPPUNIT_TEST(i<unsigned long>);
+    CPPUNIT_TEST(i<float>);
+    CPPUNIT_TEST(i<double>);
     CPPUNIT_TEST_SUITE_END();
 };
 CPPUNIT_TEST_SUITE_REGISTRATION(VariableMatrixTest);