Timeline for Rotation of Pauli Vectors with $SU(2)$ reproduces the $SO(3)$ matrix. but do all $SU(2)$ matrices reproduces $SO(3)$?

9 events

when toggle format	what		by	license	comment
May 16 at 23:15	history	edited	Cosmas Zachos	CC BY-SA 4.0	added 53 characters in body
May 16 at 19:45	comment	added	Cosmas Zachos		WP.
May 16 at 19:39	comment	added	abx_pradB		So Just an analogy I am making here. like how the $SU(2)$ maps to $SO(3)$ and double covers it. we can say that $SL(2,C)$ maps to $SO^+(1,3)$ and double covers it ryt?
May 16 at 19:35	history	edited	Cosmas Zachos	CC BY-SA 4.0	added 10 characters in body
May 16 at 19:34	comment	added	abx_pradB		So every SU(2) does gives rise to SO(3). since determinant becomes 1, as I checked
May 16 at 19:33	vote	accept	abx_pradB
May 16 at 19:28	comment	added	Cosmas Zachos		I haven't thought about it, but take the determinant. Many of these statements are trivial to verify for small rotations, near the identity.
May 16 at 19:25	comment	added	abx_pradB		ok so it turns to be real orthogonal but how to confirm that it is a rotation and not reflection?
May 16 at 19:13	history	answered	Cosmas Zachos	CC BY-SA 4.0