矩阵乘法性质

main.cpp

@@ -5,43 +5,49 @@
 
 int main() {
 
-	GVector3 v1(SQRT(2)/2, SQRT(2) / 2, 0);
-	GVector3 v2(-1, 1, -1);
-	GVector3 v3(0, -2, -2);
-
-	//斯密特正交化
-	GVector3 w1 = v1;
-	GVector3 w2 = v2 - proj(v2, w1);  //cout << w2 << endl;
-	GVector3 w3 = v3 - proj(v3, w1) - proj(v3, w2); //cout << w3 << endl;
+	/*
+	matrix P = （p1, p2, p3, ......, pn）
+	matrix A;
+	A * P = (A*p1, A*p2, A*p3, ......, A*pn)
+	*/
+	float a[] = {
+		3, -1, 0,
+		4, -1, 0,
+		-1, 0, 0
+	};
+	GMatrix A(3, 3, a);
 
-	//normalize
-	w1 = w1 / norm(w1);
-	w2 = w2 / norm(w2);
-	w3 = w3 / norm(w3);
+	float p[] = {
+		1, 2, 3,
+		1, 2, 3,
+		1, 2, 3
+	};
+	GMatrix P(3, 3, p);
 
-	GMatrix M1(3, 3);
-	M1.SetRowVec(0, w1);
-	M1.SetRowVec(1, w2);
-	M1.SetRowVec(2, w3);
-	cout << M1 << endl;
+	//模拟P矩阵的第二列
+	float x[] = {
+		2,
+		2,
+		2
+	};
+	GMatrix X(3, 1, x);
 
-	GMatrix M2 = Transpose(M1);
-	cout << M2 << endl;
+	cout << A * P << endl;
+	cout << A * X << endl;
 
-	cout << Det(M1) * Det(M2) << endl;
+	/*
+	matrix P = （p1, p2, p3, ......, pn）
+	vector v = （v1, v2, v3, ......, vn）
 
-	float a[] = {
-		1, 2, 3,
-		3, 1, 2,
-		2, 3, 1
-	};
-	GMatrix M3(3, 3, a);
+	P * V = (p1 * v1) + (p2 * v2) + (p3 * v3) + ...... + (pn * vn)
+	*/
+	GVector c1 = A.GetColVec(0);
+	GVector c2 = A.GetColVec(1);
+	GVector c3 = A.GetColVec(2);
 
-	GMatrix M4 = Inverse(M3);
+	GVector ret = c1 * X[0][0] + c2 * X[1][0] + c3 * X[2][0];
+	cout << ret << endl;
 	
-	cout << M3 << endl;
-	cout << M4 << endl;
 
-	cout << Det(M3) * Det(M4) << endl;
   	return 0;
 }