Application 1:Givens rotation Outline Unitary and Orthogonal Matrices Application 1:Givens rotation Application 2:Permutation matrix Discovery Journey References 色电有这女子 Matrix Theory Special Matrices -4/23
Application 1: Givens rotation Outline Unitary and Orthogonal Matrices Application 1: Givens rotation Application 2: Permutation matrix Discovery Journey References Matrix Theory Special Matrices - 4/23
Application 1:Givens rotation Givens rotation 奇电有这头 Matrix Theory S Special Matrices -5/23
Application 1: Givens rotation Givens rotation Let c and s be scalars with ∣c∣ 2 + ∣s∣ 2 = 1. The matrices ( c s −s c ) , ( c s s −c ) are unitary. Matrix Theory Special Matrices - 5/23
Application 1:Givens rotation Givens rotation Let c and s be scalars with c2+ls2=1. 命电有这女子 Matrix Theory Special Matrices -5/23
Application 1: Givens rotation Givens rotation Let c and s be scalars with ∣c∣ 2 + ∣s∣ 2 = 1. The matrices ( c s −s c ) , ( c s s −c ) are unitary. Matrix Theory Special Matrices - 5/23
Application 1:Givens rotation Givens rotation Let c and s be scalars with 1c2+ls2=1. The matrices (5)() are unitary. 命电有这女子 Matrix Theory Special Matrices -5/23
Application 1: Givens rotation Givens rotation Let c and s be scalars with ∣c∣ 2 + ∣s∣ 2 = 1. The matrices ( c s −s c ) , ( c s s −c ) are unitary. Matrix Theory Special Matrices - 5/23
Application 1:Givens rotation Definition If c,seC so that lc2+ls2=1, 命电有这女子 Matrix Theory Special Matrices -6/23
Application 1: Givens rotation Definition If c,s ∈ C so that ∣c∣ 2 + ∣s∣ 2 = 1, then the unitary 2 × 2 matrix ( c s −s c ) is called a Givens rotation. If c and s are also real, then the Givens rotation ( c s −s c ) is orthogonal. Matrix Theory Special Matrices - 6/23