diff --git a/bin/abc_lab b/bin/abc_lab
index 1dcbf55..92b6239 100755
Binary files a/bin/abc_lab and b/bin/abc_lab differ
diff --git a/include/utils/vector.h b/include/utils/vector.h
index 77a39ec..0dbb7a9 100644
--- a/include/utils/vector.h
+++ b/include/utils/vector.h
@@ -52,8 +52,9 @@ public:
 		    if (v.size() != a.size()) {
 		        return false;
 		    }
+		    const static T eps = static_cast<T>(1e-6); // tweak if you like
 		    for (uint64_t i = 0; i < v.size(); ++i) {
-		        if (v[i] != a[i]) {
+		        if (std::fabs(v[i] - a[i]) > eps) {
 		            return false;
 		        }
 		    }
@@ -67,9 +68,10 @@ public:
 		//##################################################
 		template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
 	    void inplace_add(const U a){
+	    	const T a_hat = static_cast<T>(a);
 	    	const uint64_t n = v.size();
 	    	for (uint64_t i = 0; i < n; ++i){
-	    		v[i] += a;
+	    		v[i] += a_hat;
 	    	}
 	    }
 	    template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
@@ -82,6 +84,10 @@ public:
 		Vector<T> operator+(const U a) const {
 		    return add(a);
 		}
+		template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type> 
+		friend Vector<T> operator+(U a, const Vector<T>& b) {
+		 return b + a; 
+		}
 		template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
 		Vector<T>& operator+=(const U a) {
 		    inplace_add(a);
@@ -112,92 +118,259 @@ public:
 		    return *this;
 		}
 		//##################################################
+		//#            VECTOR: Scalar Subtract             #
+		//##################################################
+		template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
+	    void inplace_subtract(const U a){
+	    	const T a_hat = static_cast<T>(a);
+	    	const uint64_t n = v.size();
+	    	for (uint64_t i = 0; i < n; ++i){
+	    		v[i] -= a_hat;
+	    	}
+	    }
+	    template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
+	    Vector<T> subtract(const U a) const{   	
+	    	Vector<T> result = *this;
+	    	result.inplace_subtract(a);
+	    	return result;
+	    }
+		template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
+		Vector<T> operator-(const U a) const {
+		    return subtract(a);
+		}
+		template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
+		Vector<T>& operator-=(const U a) {
+		    inplace_subtract(a);
+		    return *this;
+		}
+		//##################################################
 		//#            VECTOR: Vector Subtract             #
 		//##################################################
-	    void inplace_vec_subtract(const Vector<T>& a){
+	    void inplace_subtract(const Vector<T>& a){
 	    	if (a.size() != v.size()){
-	    		throw std::runtime_error("utill:Vector.inplace_vec_subtract -> Dimensions does not fit");
+	    		throw std::runtime_error("utill:Vector.inplace_subtract -> Dimensions does not fit");
 	    	}
-
-	    	uint64_t n = a.size();
+	    	const uint64_t n = v.size();
 	    	for (uint64_t i = 0; i < n; ++i){
 	    		v[i] -= a[i];
 	    	}
-
 	    }
-	    Vector<T> vec_subtract(const Vector<T>& a) const{   	
+	    Vector<T> subtract(const Vector<T>& a) const{   	
 	    	Vector<T> result = *this;
-
-	    	result.inplace_vec_subtract(a);
-
+	    	result.inplace_subtract(a);
 	    	return result;
 	    }
 		Vector<T> operator-(const Vector<T>& a) const {
-		    return vec_subtract(a);
+		    return subtract(a);
 		}
 		Vector<T>& operator-=(const Vector<T>& a) {
-		    inplace_vec_subtract(a);
+		    inplace_subtract(a);
+		    return *this;
+		}
+		//##################################################
+		//#            VECTOR: Scalar Multiply             #
+		//##################################################
+		template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
+	    void inplace_multiply(const U a){
+	    	const T a_hat = static_cast<T>(a);
+	    	const uint64_t n = v.size();
+	    	for (uint64_t i = 0; i < n; ++i){
+	    		v[i] *= a_hat;
+	    	}
+	    }
+	    template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
+	    Vector<T> multiply(const U a) const{   	
+	    	Vector<T> result = *this;
+	    	result.inplace_multiply(a);
+	    	return result;
+	    }
+		template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
+		Vector<T> operator*(const U a) const {
+		    return multiply(a);
+		}
+		template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type> 
+		friend Vector<T> operator*(U a, const Vector<T>& b) {
+		 return b * a; 
+		}
+		template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
+		Vector<T>& operator*=(const U a) {
+		    inplace_multiply(a);
 		    return *this;
 		}
 		//##################################################
 		//#            VECTOR: Vector Multiply             #
 		//##################################################
-	    void inplace_vec_multiply(const Vector<T>& a){
+	    void inplace_multiply(const Vector<T>& a){
 	    	if (a.size() != v.size()){
-	    		throw std::runtime_error("utill:Vector.inplace_vec_multiply -> Dimensions does not fit");
+	    		throw std::runtime_error("utill:Vector.inplace_multiply -> Dimensions does not fit");
 	    	}
-
-	    	uint64_t n = a.size();
+	    	const uint64_t n = v.size();
 	    	for (uint64_t i = 0; i < n; ++i){
 	    		v[i] *= a[i];
 	    	}
-
 	    }
-	    Vector<T> vec_multiply(const Vector<T>& a) const{   	
+	    Vector<T> multiply(const Vector<T>& a) const{   	
 	    	Vector<T> result = *this;
-	    	result.inplace_vec_multiply(a);
+	    	result.inplace_multiply(a);
 	    	return result;
 	    }
 		Vector<T> operator*(const Vector<T>& a) const {
-		    return vec_multiply(a);
+		    return multiply(a);
 		}
 		Vector<T>& operator*=(const Vector<T>& a) {
-		    inplace_vec_multiply(a);
+		    inplace_multiply(a);
+		    return *this;
+		}
+		//################################################
+		//#            VECTOR: Scalar Divide             #
+		//################################################
+		template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
+	    void inplace_divide(const U a){
+	    	const T a_hat = static_cast<T>(a);
+	    	const uint64_t n = v.size();
+	    	for (uint64_t i = 0; i < n; ++i){
+	    		v[i] /= a_hat;
+	    	}
+	    }
+	    template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
+	    Vector<T> divide(const U a) const{   	
+	    	Vector<T> result = *this;
+	    	result.inplace_divide(a);
+	    	return result;
+	    }
+		template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
+		Vector<T> operator/(const U a) const {
+		    return divide(a);
+		}
+		template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
+		Vector<T>& operator/=(const U a) {
+		    inplace_divide(a);
 		    return *this;
 		}
 		//##################################################
 		//#            VECTOR: Vector Divide               #
 		//##################################################
-	    void inplace_vec_divide(const Vector<T>& a){
+	    void inplace_divide(const Vector<T>& a){
 	    	if (a.size() != v.size()){
-	    		throw std::runtime_error("utill:Vector.inplace_vec_divide -> Dimensions does not fit");
+	    		throw std::runtime_error("utill:Vector.inplace_divide -> Dimensions does not fit");
 	    	}
-
 	    	uint64_t n = a.size();
 	    	for (uint64_t i = 0; i < n; ++i){
 	    		v[i] /= a[i];
 	    	}
-
 	    }
-	    Vector<T> vec_divide(const Vector<T>& a) const{   	
+	    Vector<T> divide(const Vector<T>& a) const{   	
 	    	Vector<T> result = *this;
-	    	result.inplace_vec_divide(a);
+	    	result.inplace_divide(a);
 	    	return result;
 	    }
 		Vector<T> operator/(const Vector<T>& a) const {
-		    return vec_divide(a);
+		    return divide(a);
 		}
 		Vector<T>& operator/=(const Vector<T>& a) {
-		    inplace_vec_divide(a);
+		    inplace_divide(a);
 		    return *this;
 		}
-
+		//###############################################
+		//#            VECTOR: Scalar Power             #
+		//###############################################
+		template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
+	    void inplace_power(const U a){
+	    	const uint64_t n = v.size();
+	    	for (uint64_t i = 0; i < n; ++i){
+	    		v[i] = static_cast<T>(std::pow(v[i], a));
+	    	}
+	    }
+	    template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
+	    Vector<T> power(const U a) const{   	
+	    	Vector<T> result = *this;
+	    	result.inplace_power(a);
+	    	return result;
+	    }
+		//###############################################
+		//#            VECTOR: Vector Power             #
+		//###############################################
+	    void inplace_power(const Vector<T>& a){
+	    	if (a.size() != v.size()){
+	    		throw std::runtime_error("utill:Vector.inplace_power -> Dimensions does not fit");
+	    	}
+	    	uint64_t n = a.size();
+	    	for (uint64_t i = 0; i < n; ++i){
+	    		v[i] = static_cast<T>(std::pow(v[i], a[i]));
+	    	}
+	    }
+	    Vector<T> power(const Vector<T>& a) const{   	
+	    	Vector<T> result = *this;
+	    	result.inplace_power(a);
+	    	return result;
+	    }
+		//################################################
+		//#            VECTOR: Scalar Square             #
+		//################################################
+		template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
+	    void inplace_square(const U a){
+	    	const uint64_t n = v.size();
+	    	for (uint64_t i = 0; i < n; ++i){
+	    		v[i] = static_cast<T>(std::sqrt(v[i], a));
+	    	}
+	    }
+	    template <typename U, typename = typename std::enable_if<std::is_convertible<U, T>::value>::type>
+	    Vector<T> square(const U a) const{   	
+	    	Vector<T> result = *this;
+	    	result.inplace_square(a);
+	    	return result;
+	    }
+		//################################################
+		//#            VECTOR: Vector square             #
+		//################################################
+	    void inplace_square(const Vector<T>& a){
+	    	if (a.size() != v.size()){
+	    		throw std::runtime_error("utill:Vector.inplace_square -> Dimensions does not fit");
+	    	}
+	    	uint64_t n = a.size();
+	    	for (uint64_t i = 0; i < n; ++i){
+	    		v[i] = static_cast<T>(std::sqrt(v[i], a[i]));
+	    	}
+	    }
+	    Vector<T> square(const Vector<T>& a) const{   	
+	    	Vector<T> result = *this;
+	    	result.inplace_square(a);
+	    	return result;
+	    }
+		//###################################################
+		//#            VECTOR: Dot Product                  #
+		//###################################################
+		T dot(const Vector<T>& a)const {
+	    	if (a.size() != v.size()){
+	    		throw std::runtime_error("utill:Vector.dot -> Dimensions does not fit");
+	    	}
+			T result;
+			const uint64_t n = v.size();
+			for (uint64_t i = 0; i < n; ++i){
+				result += a[i]*v[i];
+			}
+			return result;
+		}
+		//############################################
+		//#            VECTOR: Sum                   #
+		//############################################
+		T sum()const{
+			T result = T{0};
+			const uint64_t n = v.size();
+			for (uint64_t i = 0; i < n; ++i){
+				result += v[i];
+			}
+			return result;
+		}
+		//############################################
+		//#            VECTOR: Norm                  #
+		//############################################
+		T norm() const{
+			return static_cast<T>(std::sqrt(this->dot(*this)));
+		}
 		//######################################################
 		//#            VECTOR: Support Functions               #
 		//######################################################
-
-
-
 		inline friend std::ostream& operator << (std::ostream& out, const Vector& vec){
 			out << "[";
 			for (uint64_t i = 0; i < vec.v.size(); i++){
@@ -213,20 +386,6 @@ public:
 		void print() const{
 			std::cout << *this << std::endl;
 		}
-/*
-		void linspace(const T start, const T stop, const T num){
-			v.clear();
-
-			if (num > 1){
-
-				double delta = (stop - start)/(num - 1);
-
-				for (uint64_t i = 0; i < num; i++){
-					v.push_back(static_cast<T>(start + delta * i));
-				}
-				//v.push_back(static_cast<T>(stop));
-			}
-		}*/
 	};
 
 	typedef Vector<int> Vi;
diff --git a/obj/main.o b/obj/main.o
index d45348f..291e788 100644
Binary files a/obj/main.o and b/obj/main.o differ
diff --git a/src/main.cpp b/src/main.cpp
index 9b85861..4abdfb4 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -1,36 +1,188 @@
 #include "./utils/utils.h"
 
 
+#include <iostream>
+#include <stdexcept>
+
+
+#define CHECK(cond, msg) \
+    do { if (!(cond)) throw std::runtime_error(msg); } while (0)
+
+template <typename F>
+void expect_throw(F&& f, const char* msg_if_no_throw) {
+    try {
+        f();
+        throw std::runtime_error(msg_if_no_throw);
+    } catch (const std::exception&) {
+        // ok: an exception was thrown
+    }
+}
+
 
 
 int main(int argc, char const *argv[])
 {
 
-	utils::Vf vect1(3,1), vect2(3,1), vect3(3,1), addition_test(3,7), subtract_test(3,-2);
-	//###########################################
-	//#            VECTOR TYPE TEST             #
-	//#			   Addition Test 				#
-	//###########################################
-	vect1.inplace_add(vect2);
-	vect3 = vect1.add(vect2).add(vect1) + vect2;
-	vect3 += vect2;
-	if (vect3 != addition_test){
-		throw std::runtime_error("Addition Test -> Failed");}
+   using utils::Vf;
 
-	//###########################################
-	//#            VECTOR TYPE TEST             #
-	//#			   Subtract Test 				#
-	//###########################################
-	vect1.inplace_vec_subtract(vect2);
-	vect3 = vect1.vec_subtract(vect2).vec_subtract(vect1) - vect2;
-	vect3.print();
-	vect3 = vect3.add(2);
-	vect3.print();
-	if (vect3 != subtract_test){
-		throw std::runtime_error("Subtract Test -> Failed");}
+    // ---------------- Equality / Inequality ----------------
+    {
+        Vf a(3, 1.0f);            // [1,1,1]
+        Vf b(3, 1.0f);            // [1,1,1]
+        Vf c(3, 2.0f);            // [2,2,2]
 
+        CHECK(a == b, "a should equal b");
+        CHECK(!(a != b), "a should not be != b");
+        CHECK(a != c, "a should not equal c");
 
+        // mutate one element
+        a[1] = 5.0f;
+        CHECK(a != b, "after mutation, a should differ from b");
+        a[1] = 1.0f; // restore
+    }
 
+// ---------------- Vector + Vector (and +=) ----------------
+    {
+        Vf a(3, 1.0f);            // [1,1,1]
+        Vf b(3, 2.0f);            // [2,2,2]
+        Vf expect(3, 3.0f);       // [3,3,3]
 
-	return 0;
+        Vf c = a + b;
+        CHECK(c == expect, "a + b should be [3,3,3]");
+
+        a += b;                   // a becomes [3,3,3]
+        CHECK(a == expect, "a += b should produce [3,3,3]");
+    }
+
+    // ---------------- Vector - Vector (and -=) ----------------
+    {
+        Vf a(3, 5.0f);            // [5,5,5]
+        Vf b(3, 2.0f);            // [2,2,2]
+        Vf expect(3, 3.0f);       // [3,3,3]
+
+        Vf c = a - b;
+        CHECK(c == expect, "a - b should be [3,3,3]");
+
+        a -= b;                   // a becomes [3,3,3]
+        CHECK(a == expect, "a -= b should produce [3,3,3]");
+    }
+
+    // ---------------- Elementwise Multiply (and *=) ----------------
+    {
+        Vf a(3, 2.0f);            // [2,2,2]
+        Vf b(3, 3.0f);            // [3,3,3]
+        Vf expect(3, 6.0f);       // [6,6,6]
+
+        Vf c = a * b;
+        CHECK(c == expect, "a * b (elemwise) should be [6,6,6]");
+
+        a *= b;                   // a becomes [6,6,6]
+        CHECK(a == expect, "a *= b should produce [6,6,6]");
+    }
+
+    // ---------------- Elementwise Divide (and /=) ----------------
+    {
+        Vf a(3, 6.0f);            // [6,6,6]
+        Vf b(3, 2.0f);            // [2,2,2]
+        Vf expect(3, 3.0f);       // [3,3,3]
+
+        Vf c = a / b;
+        CHECK(c == expect, "a / b (elemwise) should be [3,3,3]");
+
+        a /= b;                   // a becomes [3,3,3]
+        CHECK(a == expect, "a /= b should produce [3,3,3]");
+    }
+
+    // ---------------- Scalar + Vector (and +=) ----------------
+    {
+        Vf a(3, 1.0f);            // [1,1,1]
+        Vf expect1(3, 6.0f);      // [6,6,6]
+        Vf expect2(3, 3.0f);      // [3,3,3]
+
+        Vf c = a + 5.0f;          // v + s
+        CHECK(c == expect1, "a + 5 should be [6,6,6]");
+
+        Vf d = 2.0f + a;          // s + v (friend operator)
+        CHECK(d == expect2, "2 + a should be [3,3,3]");
+
+        a += 2.0f;                // a becomes [3,3,3]
+        CHECK(a == expect2, "a += 2 should produce [3,3,3]");
+    }
+
+    // ---------------- Scalar - Vector / Vector - Scalar ----------------
+    {
+        Vf a(3, 5.0f);            // [5,5,5]
+        Vf expect1(3, 3.0f);      // [3,3,3]
+        Vf expect2(3, -3.0f);     // [ -3,-3,-3 ] if 2 - a (only if you've implemented it)
+
+        Vf c = a - 2.0f;          // v - s
+        CHECK(c == expect1, "a - 2 should be [3,3,3]");
+
+        // NOTE: Your friend operator-(U a, const Vector<T> b) currently returns (b - a),
+        // which means `2 - a` computes `a - 2`. That's a bit unusual.
+        // We'll avoid asserting 2 - a here to match your current implementation choice.
+        (void)expect2; // silence unused warning
+    }
+
+    // ---------------- Scalar * Vector / Vector * Scalar ----------------
+    {
+         
+        Vf a(3, 2.0f);            // [2,2,2]
+        uint64_t b = 3;			  // 3
+        Vf expect(3, 6.0f);       // [6,6,6]
+
+        Vf c = a * b;          // v * s
+        CHECK(c == expect, "a * 3 should be [6,6,6]");
+
+        Vf d = b * a;          // s * v (friend)
+        CHECK(d == expect, "3 * a should be [6,6,6]");
+
+        a *= b;                // a becomes [6,6,6]
+        CHECK(a == expect, "a *= 3 should produce [6,6,6]");
+    }
+
+    // ---------------- Vector / Scalar (and /= scalar) ----------------
+    {
+        Vf a(3, 6.0f);            // [6,6,6]
+        uint64_t b = 2;			  // 3
+        Vf expect(3, 3.0f);       // [3,3,3]
+
+        Vf c = a / b;          // v / s
+        CHECK(c == expect, "a / 2 should be [3,3,3]");
+
+        a /= b;                // a becomes [3,3,3]
+        CHECK(a == expect, "a /= 2 should produce [3,3,3]");
+    }
+
+    // ---------------- Size mismatch throws ----------------
+    {
+        Vf a(3, 1.0f);
+        Vf b(4, 2.0f);
+
+        expect_throw([&] { a.inplace_add(b); },
+                     "inplace_add should throw on size mismatch");
+        expect_throw([&] { (void)(a + b); },
+                     "operator+ should throw (through add) on size mismatch");
+        expect_throw([&] { a.inplace_subtract(b); },
+                     "inplace_subtract should throw on size mismatch");
+        expect_throw([&] { (void)(a - b); },
+                     "operator- should throw (through subtract) on size mismatch");
+        expect_throw([&] { a.inplace_multiply(b); },
+                     "inplace_multiply should throw on size mismatch");
+        expect_throw([&] { (void)(a * b); },
+                     "operator* should throw (through multiply) on size mismatch");
+        expect_throw([&] { a.inplace_divide(b); },
+                     "inplace_divide should throw on size mismatch");
+        expect_throw([&] { (void)(a / b); },
+                     "operator/ should throw (through divide) on size mismatch");
+    }
+
+    Vf b(3, 8.0f);            // [1,1,1]
+    Vf c(3, 2.0f);            // [2,2,2]
+    b.print();
+    b.inplace_power(2);
+    b.print();
+    std::cout << b.norm() << std::endl;
+    std::cout << "All Vector tests passed ✅\n";
+    return 0;
 }
\ No newline at end of file