Let H in 1 be a 2 times 2 matrix defined by w w1 w2T Show t

Let H in (1) be a 2 times 2 matrix defined by w = (w1, w2)^T. Show that H =(c s s -c) , c^2 + s^2 = 1 and give expressions for c and s terms of w_1 and w_2.

Solution

When we take determinant of the given matrix, then we will get this equation

|c(-c)-s²|=1

Take minus common,

|-(c²+s²)|=1

It will be negotiated by mode sign, we will have this final equation,

c²+s²=1

Hence it is proved.

Then c will be equal to w₁

and s will be equal to w₂