Group Actions 4

We look at three examples. Linear algebra background is required, though a quick recap is done. Timestamp provided by Amit Mittal. 0:00 : Introduction 2:00 : preliminaries , close relations between linear maps and matrix 12:10 : Example 1 , GL(n ,K) acts on K^n , matrix multiplication : exactly 2 orbits 19:42 : Example 2 , O(n ,R) acts on R^n ,matrix multiplication : orbits are concentric sphere with center at origin (so uncountably many orbits) 34:16 : Example 3 , GL(n, C) acts on M(n, C) : will continue in next lecture. 35:35 : Stabiliser of Example 1 38:45 : Stabiliser of Example 2