diff --git a/src/zutil/math/Matrix.java b/src/zutil/math/Matrix.java
index d7a3f8a..9ec3e74 100755
--- a/src/zutil/math/Matrix.java
+++ b/src/zutil/math/Matrix.java
@@ -172,6 +172,40 @@ public class Matrix {
      *                      Vector
      **********************************************************************/
 
+    /**
+     * Vector addition, every element in the first vector will be added
+     * with the corresponding element in the second vector.
+     *
+     * @return a new vector with subtracted elements
+     */
+    public static double[] add(double[] vector1, double[] vector2){
+        vectorPreCheck(vector1, vector2);
+        double[] result = new double[vector1.length];
+
+        for (int i=0; i < result.length; ++i) {
+            result[i] = vector1[i] + vector2[i];
+        }
+        return result;
+    }
+
+    /**
+     * Matrix Vector addition, every column in the matrix will be added
+     * with the vector.
+     *
+     * @return a new matrix with subtracted elements
+     */
+    public static double[][] add(double[][] matrix, double[] vector){
+        vectorPreCheck(matrix, vector);
+        double[][] result = new double[matrix.length][matrix[0].length];
+
+        for (int y=0; y < result.length; ++y) {
+            for (int x=0; x < result.length; ++x) {
+                result[y][x] = matrix[y][x] + vector[x];
+            }
+        }
+        return result;
+    }
+
     /**
      * Vector subtraction, every element in the first vector will be subtracted
      * with the corresponding element in the second vector.
@@ -188,19 +222,40 @@ public class Matrix {
         return result;
     }
 
+    /**
+     * Matrix Vector subtraction, each column in the matrix will be subtracted
+     * with the vector.
+     *
+     * @return a new vector with subtracted elements
+     */
+    public static double[][] subtract(double[][] matrix, double[] vector){
+        vectorPreCheck(matrix, vector);
+        double[][] result = new double[matrix.length][matrix[0].length];
+
+        for (int y=0; y < result.length; ++y) {
+            for (int x=0; x < result.length; ++x) {
+                result[y][x] = matrix[y][x] - vector[x];
+            }
+        }
+
+        return result;
+    }
+
     /**
      * Matrix Vector multiplication, each element column in the matrix will be
      * multiplied with the corresponding element row in the vector.
      *
      * @return a new vector with the result
      */
-    public static double[] multiply(double[][] matrix, double[] vector){
+    public static double[][] multiply(double[][] matrix, double[] vector){
         vectorPreCheck(matrix, vector);
-        double[] result = new double[matrix.length];
+        double[][] result = new double[matrix.length][1];
 
-        for (int y=0; y < matrix.length; ++y) {
-            for (int x=0; x < matrix[y].length; ++x){
-                result[y] += matrix[y][x] * vector[x];
+        for (int y=0; y < result.length; ++y) {
+            for (int x=0; x<matrix[0].length; ++x) {
+                for (int i=0; i < result[y].length; ++i){
+                    result[y][i] += matrix[y][x] * vector[x];
+                }
             }
         }
         return result;
@@ -263,10 +318,10 @@ public class Matrix {
         matrixPreCheck(matrix1, matrix2);
         double[][] result = new double[matrix1.length][matrix2[0].length];
 
-        for (int i=0; i < result.length; ++i) {
-            for (int k=0; k<matrix1[0].length; ++k) {
-                for (int j=0; j < result[i].length; ++j){
-                    result[i][j] += matrix1[i][k] * matrix2[k][j];
+        for (int y=0; y < result.length; ++y) {
+            for (int x=0; x<matrix1[0].length; ++x) {
+                for (int i=0; i < result[y].length; ++i){
+                    result[y][i] += matrix1[y][x] * matrix2[x][i];
                 }
             }
         }
@@ -323,4 +378,15 @@ public class Matrix {
         return result;
     }
 
+    /**
+     * @return a single dimension double array containing the elements of the j:th column
+     */
+    public static double[] getColumn(double[][] x, int j) {
+        double[] col = new double[x.length];
+
+        for (int i = 0; i<x.length; i++)
+            col[i] = x[i][j];
+
+        return col;
+    }
 }
diff --git a/src/zutil/ml/LinearRegression.java b/src/zutil/ml/LinearRegression.java
index 0f3cab5..d1d22e5 100755
--- a/src/zutil/ml/LinearRegression.java
+++ b/src/zutil/ml/LinearRegression.java
@@ -16,7 +16,7 @@ public class LinearRegression {
      *     h(x) = theta0 * x0 + theta1 * x1 + ... + thetan * xn => transpose(theta) * x
      * </i>
      */
-    protected static double[] calculateHypotesis(double[][] x, double[] theta){
+    protected static double[][] calculateHypotesis(double[][] x, double[] theta){
         return Matrix.multiply(x, theta);
     }
 
@@ -24,15 +24,36 @@ public class LinearRegression {
      * Linear Regresion cost method.
      * <br /><br />
      * <i>
-     *      J(O) = 1 / (2 * m) * Σ { ( h(xi) - yi )^2 }
+     *      J(O) = 1 / (2 * m) * Σ { ( h(Xi) - Yi )^2 }
      * </i><br>
      * m = learning data size (rows)
      * @return a number indicating the error rate
      */
     protected static double calculateCost(double[][] x, double[] y, double[] theta){
-        return 1 / (2 * x.length) * Matrix.sum(
+        return 1.0 / (2.0 * x.length) * Matrix.sum(
                 Matrix.Elemental.pow(
                         Matrix.subtract(calculateHypotesis(x, theta), y),
                         2));
     }
+
+    /**
+     * Gradient Descent algorithm
+     * <br /><br />
+     * <i>
+     *     Oj = Oj - α * (1 / m) *  Σ { ( h(Xi) - Yi ) * Xij }
+     * </i><br />
+     *
+     * @return the theta that was found to minimize the cost function
+     */
+    public static double[] gradientAscent(double[][] x, double[] y, double[] theta, double alpha){
+        double[] newTheta = new double[theta.length];
+        double m = y.length;
+        double[][] hypotesisCache = Matrix.subtract(calculateHypotesis(x, theta), y);
+
+        for (int j= 0; j < theta.length; j++) {
+            newTheta[j] = theta[j] - alpha * (1.0/m) * Matrix.sum(Matrix.add(hypotesisCache, Matrix.getColumn(x, j)));
+        }
+
+        return newTheta;
+    }
 }
diff --git a/test/zutil/math/MatrixTest.java b/test/zutil/math/MatrixTest.java
index e979a7e..bea2330 100755
--- a/test/zutil/math/MatrixTest.java
+++ b/test/zutil/math/MatrixTest.java
@@ -70,14 +70,46 @@ public class MatrixTest {
 
 
     @Test
-    public void vectorMultiply(){
+    public void vectorAddition(){
         assertArrayEquals(
-                new double[]{8,14},
-                Matrix.multiply(new double[][]{{2,3},{-4,9}}, new double[]{1,2}),
+                new double[]{3,5,-1,13},
+                Matrix.add(new double[]{2,3,-4,9}, new double[]{1,2,3,4}),
                 0.0
         );
     }
 
+    @Test
+    public void vectorMatrixAddition(){
+        assertArrayEquals(
+                new double[][]{{2,3,4,5},{2,3,4,5},{2,3,4,5},{2,3,4,5}},
+                Matrix.add(new double[][]{{1,2,3,4},{1,2,3,4},{1,2,3,4},{1,2,3,4}}, new double[]{1,1,1,1})
+        );
+    }
+
+    @Test
+    public void vectorSubtraction(){
+        assertArrayEquals(
+                new double[]{1,1,-7,5},
+                Matrix.subtract(new double[]{2,3,-4,9}, new double[]{1,2,3,4}),
+                0.0
+        );
+    }
+
+    @Test
+    public void vectorMatrixSubtraction(){
+        assertArrayEquals(
+                new double[][]{{0,1,2,3},{0,1,2,3},{0,1,2,3},{0,1,2,3}},
+                Matrix.subtract(new double[][]{{1,2,3,4},{1,2,3,4},{1,2,3,4},{1,2,3,4}}, new double[]{1,1,1,1})
+        );
+    }
+
+    @Test
+    public void vectorMultiply(){
+        assertArrayEquals(
+                new double[][]{{8},{14}},
+                Matrix.multiply(new double[][]{{2,3},{-4,9}}, new double[]{1,2}));
+    }
+
     @Test
     public void vectorDivision(){
         assertArrayEquals(
@@ -138,4 +170,13 @@ public class MatrixTest {
                 new double[][]{{1,0,0,0},{0,1,0,0},{0,0,1,0},{0,0,0,1}},
                 Matrix.identity(4));
     }
+
+    @Test
+    public void getColumn(){
+        assertArrayEquals(
+                new double[]{2,3,4,1},
+                Matrix.getColumn(new double[][]{{1,2,3,4},{2,3,4,1},{3,4,1,2},{4,1,2,3}}, 1),
+                0.0
+        );
+    }
 }
\ No newline at end of file
diff --git a/test/zutil/ml/LinearRegressionTest.java b/test/zutil/ml/LinearRegressionTest.java
new file mode 100755
index 0000000..4ecb21f
--- /dev/null
+++ b/test/zutil/ml/LinearRegressionTest.java
@@ -0,0 +1,44 @@
+package zutil.ml;
+
+import org.junit.Test;
+
+import static org.junit.Assert.*;
+
+/**
+ * Test cases are from the Machine Learning course on coursera.
+ * https://www.coursera.org/learn/machine-learning/discussions/all/threads/0SxufTSrEeWPACIACw4G5w
+ */
+public class LinearRegressionTest {
+
+    @Test
+    public void calculateHypotesis() {
+        double[][] hypotesis = LinearRegression.calculateHypotesis(
+                /* x */ new double[][]{{1, 2}, {1, 3}, {1, 4}, {1, 5}},
+                /* theta */ new double[]{0.1, 0.2}
+        );
+
+        assertArrayEquals(new double[][]{{0.5}, {0.7}, {0.9}, {1.1}}, hypotesis);
+    }
+
+    @Test
+    public void calculateCost() {
+        double cost = LinearRegression.calculateCost(
+                /* x */ new double[][]{{1, 2}, {1, 3}, {1, 4}, {1, 5}},
+                /* y */ new double[]{7, 6, 5, 4},
+                /* theta */ new double[]{0.1, 0.2}
+        );
+
+        assertEquals(11.9450, cost, 0.0001);
+    }
+
+    @Test
+    public void gradientAscent() {
+        double[] theta = LinearRegression.gradientAscent(
+                /* x */ new double[][]{{1, 5},{1, 2},{1, 4},{1, 5}},
+                /* y */ new double[]{1, 6, 4, 2},
+                /* theta */ new double[]{0, 0},
+                /* alpha */0.01);
+
+        assertArrayEquals(new double[]{0.032500, 0.107500}, theta, 0.000001);
+    }
+}
\ No newline at end of file