[討論] Givens Rotation: a 3x3 matrix illustration.

[aluba1 (aluba1)]

The following is the matlab code to transform

a 3x3 matrix to an upper triangualr one.

Please copy them into matlab command window line by line to see the result:

p1=0.9;
p2=p1*p1;
A=[1 p1 p2; p1 1 p1; p2 p1 1]

theta=(A(1,1)^2+A(2,1)^2)^(0.5);
theta=A(1,1)/theta;
theta=acos(theta);
B=[cos(theta) sin(theta) 0; -sin(theta) cos(theta) 0; 0 0 1];

A=B*A

theta=(A(1,1)^2+A(3,1)^2)^(0.5);
theta=A(1,1)/theta;
theta=acos(theta);
B=[cos(theta) 0 sin(theta); 0 1 0;-sin(theta) 0 cos(theta)];

A=B*A

theta=(A(2,2)^2+A(3,2)^2)^(0.5);
theta=A(2,2)/theta;
theta=acos(theta);
B=[1 0 0; 0 cos(theta) sin(theta);0 -sin(theta) cos(theta)];

A=B*A




Now you have an upper triangular matrix.

I hope this will help you to understand how Givens works.


aluba1.


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※ 編輯: aluba1          來自: 123.195.2.128        (05/21 05:27)
推 locust0923:Thanks for your help~ push the article