diff --git a/Math/Math.xcodeproj/project.pbxproj b/Math/Math.xcodeproj/project.pbxproj
index 925b4fd..d2f4354 100644
--- a/Math/Math.xcodeproj/project.pbxproj
+++ b/Math/Math.xcodeproj/project.pbxproj
@@ -9,7 +9,7 @@
 /* Begin PBXBuildFile section */
 		C005DFFE1BE1CBA700F1BD3C /* Math.h in Headers */ = {isa = PBXBuildFile; fileRef = C005DFFD1BE1CBA700F1BD3C /* Math.h */; settings = {ATTRIBUTES = (Public, ); }; };
 		C005E0051BE1CBA800F1BD3C /* Math.framework in Frameworks */ = {isa = PBXBuildFile; fileRef = C005DFFA1BE1CBA700F1BD3C /* Math.framework */; };
-		C005E00A1BE1CBA800F1BD3C /* MathTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = C005E0091BE1CBA800F1BD3C /* MathTests.swift */; };
+		C005E00A1BE1CBA800F1BD3C /* MatrixTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = C005E0091BE1CBA800F1BD3C /* MatrixTests.swift */; };
 		C005E0391BE1CC7A00F1BD3C /* Matrix.swift in Sources */ = {isa = PBXBuildFile; fileRef = C005E0381BE1CC7A00F1BD3C /* Matrix.swift */; };
 		C04449C11BE26A0700ABF046 /* Vector.swift in Sources */ = {isa = PBXBuildFile; fileRef = C04449C01BE26A0700ABF046 /* Vector.swift */; };
 /* End PBXBuildFile section */
@@ -29,7 +29,7 @@
 		C005DFFD1BE1CBA700F1BD3C /* Math.h */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.c.h; path = Math.h; sourceTree = "<group>"; };
 		C005DFFF1BE1CBA700F1BD3C /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
 		C005E0041BE1CBA800F1BD3C /* MathTests.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = MathTests.xctest; sourceTree = BUILT_PRODUCTS_DIR; };
-		C005E0091BE1CBA800F1BD3C /* MathTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = MathTests.swift; sourceTree = "<group>"; };
+		C005E0091BE1CBA800F1BD3C /* MatrixTests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = MatrixTests.swift; sourceTree = "<group>"; };
 		C005E00B1BE1CBA800F1BD3C /* Info.plist */ = {isa = PBXFileReference; lastKnownFileType = text.plist.xml; path = Info.plist; sourceTree = "<group>"; };
 		C005E0381BE1CC7A00F1BD3C /* Matrix.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Matrix.swift; sourceTree = "<group>"; };
 		C04449C01BE26A0700ABF046 /* Vector.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Vector.swift; sourceTree = "<group>"; };
@@ -86,7 +86,7 @@
 		C005E0081BE1CBA800F1BD3C /* MathTests */ = {
 			isa = PBXGroup;
 			children = (
-				C005E0091BE1CBA800F1BD3C /* MathTests.swift */,
+				C005E0091BE1CBA800F1BD3C /* MatrixTests.swift */,
 				C005E00B1BE1CBA800F1BD3C /* Info.plist */,
 			);
 			path = MathTests;
@@ -209,7 +209,7 @@
 			isa = PBXSourcesBuildPhase;
 			buildActionMask = 2147483647;
 			files = (
-				C005E00A1BE1CBA800F1BD3C /* MathTests.swift in Sources */,
+				C005E00A1BE1CBA800F1BD3C /* MatrixTests.swift in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
 		};
diff --git a/Math/Math/Matrix.swift b/Math/Math/Matrix.swift
index 01b0204..feb2684 100644
--- a/Math/Math/Matrix.swift
+++ b/Math/Math/Matrix.swift
@@ -8,6 +8,7 @@
 
 /** A square matrix. */
 public protocol Matrix {
+    /** The identity matrix. */
     static var identity: Self { get }
 
     /** Number of elements in the underlying container. */
@@ -19,9 +20,19 @@ public protocol Matrix {
      */
     static var dimension: Int { get }
 
+    /** Initialize a Matrix filled with zeroes. */
     init()
+
+    /** 
+     * Initialize a Matrix with a given array of values. The number of values
+     * must match the count of the array; otherwise, a MatrixError.InvalidSize
+     * error is thrown.
+     */
     init(values: [Float]) throws
 
+    /** The underlying data array. */
+    var data: [Float] { get }
+
     /** 
      * Element access
      * @{
@@ -52,7 +63,7 @@ public struct Matrix4: Matrix {
         return matrix
     }()
 
-    private var data: [Float]
+    public private(set) var data: [Float]
 
     public init() {
         data = [Float](count: Matrix4.count, repeatedValue: Float(0))
@@ -65,6 +76,7 @@ public struct Matrix4: Matrix {
         data = values
     }
 
+
     public static var dimension: Int {
         return 4
     }
@@ -102,7 +114,7 @@ public struct Matrix3: Matrix {
         return matrix
     }()
 
-    private var data: [Float]
+    public private(set) var data: [Float]
 
     public init() {
         data = [Float](count: Matrix3.count, repeatedValue: Float(0))
@@ -139,7 +151,7 @@ public struct Matrix3: Matrix {
 
     /** Convert a (row, col) pair into an index into the data array. */
     private func indexFromCoordinates(row: Int, _ col: Int) -> Int {
-        return row * Matrix4.dimension + col
+        return row * Matrix3.dimension + col
     }
 }
 
diff --git a/Math/MathTests/MathTests.swift b/Math/MathTests/MathTests.swift
deleted file mode 100644
index b345c9f..0000000
--- a/Math/MathTests/MathTests.swift
+++ /dev/null
@@ -1,36 +0,0 @@
-//
-//  MathTests.swift
-//  MathTests
-//
-//  Created by Eryn Wells on 10/28/15.
-//  Copyright © 2015 Eryn Wells. All rights reserved.
-//
-
-import XCTest
-@testable import Math
-
-class MathTests: XCTestCase {
-
-    override func setUp() {
-        super.setUp()
-        // Put setup code here. This method is called before the invocation of each test method in the class.
-    }
-
-    override func tearDown() {
-        // Put teardown code here. This method is called after the invocation of each test method in the class.
-        super.tearDown()
-    }
-
-    func testExample() {
-        // This is an example of a functional test case.
-        // Use XCTAssert and related functions to verify your tests produce the correct results.
-    }
-
-    func testPerformanceExample() {
-        // This is an example of a performance test case.
-        self.measureBlock {
-            // Put the code you want to measure the time of here.
-        }
-    }
-
-}
diff --git a/Math/MathTests/MatrixTests.swift b/Math/MathTests/MatrixTests.swift
new file mode 100644
index 0000000..749e8b6
--- /dev/null
+++ b/Math/MathTests/MatrixTests.swift
@@ -0,0 +1,108 @@
+//
+//  MathTests.swift
+//  MathTests
+//
+//  Created by Eryn Wells on 10/28/15.
+//  Copyright © 2015 Eryn Wells. All rights reserved.
+//
+
+import XCTest
+@testable import Math
+
+class Matrix4Tests: XCTestCase {
+    func testThatItHasProperDimension() {
+        XCTAssertEqual(Matrix4.dimension, 4)
+    }
+
+    func testThatItHasProperCount() {
+        XCTAssertEqual(Matrix4.count, 16)
+        XCTAssertEqual(Matrix4().data.count, Matrix4.count)
+    }
+}
+
+class Matrix4SubscriptTests: XCTestCase {
+    var m: Matrix4! = nil
+
+    override func setUp() {
+        do {
+            m = try Matrix4(values: [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15])
+        } catch {
+            XCTFail()
+        }
+    }
+
+    func testThatSingleSubscriptWorks() {
+        for i in 0..<Matrix4.count {
+            XCTAssertEqual(m[i], m.data[i])
+        }
+    }
+
+    func testThatRowColumnSubscriptWorks() {
+        var value: Int = 0
+        for i in 0..<Matrix4.dimension {
+            for j in 0..<Matrix4.dimension {
+                XCTAssertEqual(m[i,j], Float(value++))
+            }
+        }
+    }
+
+    func testThatSingleSubscriptAssignmentWorks() {
+        m[6] = 42.0
+        XCTAssertEqual(m[6], 42.0)
+    }
+
+    func testThatRowColumnSubscriptAssignmentWorks() {
+        m[1,2] = 42.0
+        XCTAssertEqual(m[1,2], 42.0)
+    }
+}
+
+class Matrix3Tests: XCTestCase {
+    func testThatItHasProperDimension() {
+        XCTAssertEqual(Matrix3.dimension, 3)
+    }
+
+    func testThatItHasProperCount() {
+        XCTAssertEqual(Matrix3.count, 9)
+        XCTAssertEqual(Matrix3().data.count, Matrix3.count)
+    }
+}
+
+class Matrix3SubscriptTests: XCTestCase {
+    var m: Matrix3! = nil
+
+    override func setUp() {
+        m = Matrix3()
+        for i in 0..<Matrix3.count {
+            m[i] = Float(i)
+        }
+    }
+
+    func testThatSingleSubscriptWorks() {
+        for i in 0..<Matrix3.count {
+            XCTAssertEqual(m[i], m.data[i])
+        }
+    }
+
+    func testThatRowColumnSubscriptWorks() {
+        XCTAssertEqual(m[0,0], m.data[0])
+        XCTAssertEqual(m[0,1], m.data[1])
+        XCTAssertEqual(m[0,2], m.data[2])
+        XCTAssertEqual(m[1,0], m.data[3])
+        XCTAssertEqual(m[1,1], m.data[4])
+        XCTAssertEqual(m[1,2], m.data[5])
+        XCTAssertEqual(m[2,0], m.data[6])
+        XCTAssertEqual(m[2,1], m.data[7])
+        XCTAssertEqual(m[2,2], m.data[8])
+    }
+
+    func testThatSingleSubscriptAssignmentWorks() {
+        m[6] = 42.0
+        XCTAssertEqual(m[6], 42.0)
+    }
+
+    func testThatRowColumnSubscriptAssignmentWorks() {
+        m[1,2] = 42.0
+        XCTAssertEqual(m[1,2], 42.0)
+    }
+}