[Eigen] 아이겐을 사용한 선형대수 복습 1일차

norm : distance of vector

    v3d::t v;
    v << -3, 2, 1; 
 
    co(v.norm() * v.norm(),"v.norm() * v.norm()");
 

unit vector : vector which of norm is one.

v3d::t v;
    v << -3, 2, 1;
 
    co(v.norm() * v.norm(),"v.norm() * v.norm()");
 
    v3d::t unitVector;
 
    unitVector = 1 / v.norm() * v;
 
    co(unitVector, "unitVector");
    co(unitVector.norm(), "unitVector.norm()");

these kind of operations referred as a normalizing

standard unit vector : vector of same direction with axis in 2D or 3D space which of norm is one.i.e..(1,0,0) , (0,1,0), (0,0,1)

cos theta from inner production between two vectors :

 
    v3d::t v1;
    v3d::t v2;
    v1 << 0, 0, 1;
    v2 << 0, 2, 2;
 
    co(v1.norm() ,"v1.norm()  ");
    co(v2.norm() ,"v2.norm()  ");
    co(v1.dot(v2),"v1.dot(v2) ");
 
    co( deg_rad(acos(v1.dot(v2) / (v1.norm() * v2.norm())) )   , "cosin Theta ") ;
 

result :

v1.norm()   = 
1
v2.norm()   = 
2.82843
v1.dot(v2)  = 
2
cosin Theta  = 
45