Diagonalisation of matrices
General · Mathematics
Study notes
Q: Diagonalize [[2,1],[1,2]] and compute A¹⁰. Eigen: 3 ((1,1)), 1 ((1,-1)). P = [[1,1],[1,-1]], D = [[3,0],[0,1]]. A = PDP⁻¹ ✓. A¹⁰ = PD¹⁰P⁻¹: D¹⁰ = [[3¹⁰,0],[0,1]]. Compute: P⁻¹ = (1/2)[[1,1],[1,-1]]. A¹⁰ = (1/2)[[3¹⁰+1,3¹⁰-1],[3¹⁰-1,3¹⁰+1]]!