diff --git a/Math/Matrix/InverseType.php b/Math/Matrix/InverseType.php
new file mode 100644
index 000000000..47b9ccdd0
--- /dev/null
+++ b/Math/Matrix/InverseType.php
@@ -0,0 +1,34 @@
+<?php
+/**
+ * Orange Management
+ *
+ * PHP Version 7.0
+ *
+ * @category   TBD
+ * @package    TBD
+ * @author     OMS Development Team <dev@oms.com>
+ * @author     Dennis Eichhorn <d.eichhorn@oms.com>
+ * @copyright  2013 Dennis Eichhorn
+ * @license    OMS License 1.0
+ * @version    1.0.0
+ * @link       http://orange-management.com
+ */
+namespace phpOMS\Math\Matrix;
+
+use phpOMS\Datatypes\Enum;
+
+/**
+ * Account type enum.
+ *
+ * @category   Framework
+ * @package    phpOMS\DataStorage\Database
+ * @author     OMS Development Team <dev@oms.com>
+ * @author     Dennis Eichhorn <d.eichhorn@oms.com>
+ * @license    OMS License 1.0
+ * @link       http://orange-management.com
+ * @since      1.0.0
+ */
+abstract class InverseType extends Enum
+{
+    const GAUSS_JORDAN = 0;
+}
diff --git a/Math/Matrix/Matrix.php b/Math/Matrix/Matrix.php
index 1963c4503..027e7ba76 100644
--- a/Math/Matrix/Matrix.php
+++ b/Math/Matrix/Matrix.php
@@ -160,4 +160,178 @@ class Matrix implements ArrayAccess, Iterator
 
         return $newMatrix;
     }
+
+    public function upperTriangular() : Matrix 
+    {
+        $matrix = new Matrix($this->n, $this->n);
+
+        $matrixArr = $this->matrix;
+        $matrix->setMatrix($this->upperTrianglize($matrixArr));
+
+        return $matrix;
+    }
+
+    public function lowerTriangular() : Matrix 
+    {
+        // todo: implement
+        return new Matrix($this->m, $this->n);
+    }
+
+    public function diag() : Matrix
+    {
+
+    }
+
+    public function inverse(int $algorithm = InversionType::GAUSS_JORDAN) : Matrix
+    {
+        if($this->n !== $this->m) {
+            throw new \Exception('Dimension');
+        }
+
+        switch($algorithm) {
+            case InversionType::GAUSS_JORDAN:
+                return $this->inverseGaussJordan();
+            default:
+                throw new \Exception('');
+        }
+    }
+
+    private function inverseGaussJordan() : Matrix
+    {
+        $newMatrixArr = $this->matrix;
+
+        // extending matrix by identity matrix
+        for($i = 0; $i < $this->n; $i++) {
+            for($j = $this->n; $j < $this->n * 2; $j++) {
+
+                if($j === ($i + $this->n)) {
+                    $newMatrixArr[$i][$j] = 1;
+                } else {
+                    $newMatrixArr[$i][$j] = 0;
+                }
+            }
+        }
+
+        // todo: maybe replace by triangulize/vice versa????!!!?!?!
+        // pivoting
+        for($i = $this->n - 1; $i > 0; $i--) {
+            if ($newMatrixArr[$i - 1][0] < $newMatrixArr[$i][0]) {
+                for($j = 0; $j < $this->n * 2; $j++) {
+                    $temp = $newMatrixArr[$i][$j];
+                    $newMatrixArr[$i][$j] = $newMatrixArr[$i-1][$j];
+                    $newMatrixArr[$i-1][$j] = $temp;
+                }
+            }
+        }
+
+        /* create diagonal matrix */
+        for($i = 0; $i < $this->n; $i++) {
+            for($j = 0; $j < $this->n; $j++) {
+                if ($j !== $i) {
+                    $temp = $newMatrixArr[$j][$i] / $newMatrixArr[$i][$i];
+
+                    for($c = 0; $c < $this->n * 2; $c++) {
+                        $newMatrixArr[$j][$c] -= $newMatrixArr[$i][$c] * $temp;
+                    }
+                }
+            }
+        }
+
+        /* create unit matrix */
+        for($i = 0; $i < $this->n; $i++) {
+            $temp = $newMatrixArr[$i][$i];
+
+            for($j = 0; $j < $this->n * 2; $j++) {
+                $newMatrixArr[$i][$j] = $newMatrixArr[$i][$j] / $temp;
+            }
+        }
+
+        /* removing identity matrix */
+        for($i = 0; $i < $this->n; $i++) {
+            $newMatrixArr[$i] = array_slice($newMatrixArr[$i], $this->n);
+        }
+
+        $newMatrix = new Matrix($this->n, $this->n);
+        $newMatrix->setMatrix($newMatrixArr);
+
+        return $newMatrix;
+    }
+
+    private function decompositionCholesky() : Matrix 
+    {
+        $newMatrix = new Matrix($this->n, $this->n);
+        $newMatrixArr = $newMatrix->getMatrix();
+
+        for ($i = 0; $i < $this->n; $i++) {
+            for ($j = 0; $j < $i+1; $j++) {
+                $temp = 0;
+
+                for ($c = 0; $c < $j; $c++) {
+                    $temp += $newMatrixArr[$i][$c] * $newMatrixArr[$j][$c];
+                }
+
+                $newMatrixArr[$i][$j] = ($i == $j) ? sqrt($this->matrix[$i][$i] - $temp) : (1 / $newMatrixArr[$j][$j] * ($this->matrix[$i][$j] - $temp));
+            }
+        }
+
+        $newMatrix->setMatrix($newMatrixArr);
+
+        return $newMatrix;
+    }
+
+    private function upperTrianglize(array &$arr) : int
+    {
+        $n = count($arr);
+        $sign = 1;
+
+        for ($i = 0; $i < $n; $i++) {
+            $max = 0;
+     
+            for ($j = $i; $j < $n; $j++) {
+                if (abs($arr[$j][$i]) > abs($arr[$max][$i])) {
+                    $max = $j;
+                }
+            }
+     
+            if ($max) {
+                $sign = -$sign;
+                $temp = $arr[$i];
+                $arr[$i] = $arr[$max], $arr[$max] = $temp;
+            }
+     
+            if (!$arr[$i][$i]) {
+                return 0;
+            }
+     
+            for ($j = $i + 1; $j < $n; $j++) {
+                $r = $arr[$j][$i] / $arr[$i][$i];
+
+                if (!$r) {
+                    continue;
+                }
+     
+                for ($c = $i; $c < $n; $c ++) {
+                    $arr[$j][$c] -= $arr[$i][$c] * $r;
+                }
+            }
+        }
+
+        return $sign;
+    } 
+
+    public function det()
+    {
+        if($this->n === 1) {
+            return $this->matrix[0][0];
+        }
+
+        $trianglize = $this->matrix;
+        $prod = $this->(upperTrianglize($trianglize));
+
+        for($i = 0; $i < $this->n; $i++) {
+            $prod *= $trianglize[$i][$i];
+        }
+
+        return $prod;
+    }
 }
\ No newline at end of file