Application 1:Givens rotation Definition If c,seC so that 1c2+ls2=1, then the unitary 2 x 2 matrix (9) is called a Givens rotation. 奇电有头子 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
Application 1:Givens rotation Definition If c,seC so that 1c2+ls2=1, then the unitary 2 x 2 matrix () is called a Givens rotation. If c and s are also real,then the Givens rotation (5) is orthogonal. 奇电年这女了 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
Application 1:Givens rotation Some remarks When a Givens rotation is real,then both diagonal elements are the same. 命电有这女子 Matrix Theory Special Matrices -7/23
Application 1: Givens rotation Some remarks ▸ When a Givens rotation is real, then both diagonal elements are the same. ▸ When a Givens rotation is complex, then the diagonal elements are complex conjugates of each other. ▸ A unitary matrix of the form ( −c s s c ) where the real parts of the diagonal elements have different signs, is a reflection; it is not a Givens rotation. In numerical linear algebra, a Givens rotation is a rotation in the plane spanned by two coordinates axes. ––Givens rotations are named after Wallace Givens, who introduced them to numerical analysts in the 1950s while he was working at Argonne National Laboratory. Matrix Theory Special Matrices - 7/23
Application 1:Givens rotation Some remarks When a Givens rotation is real,then both diagonal elements are the same. When a Givens rotation is complex,then the diagonal elements are complex conjugates of each other. 命电有这女子 Matrix Theory Special Matrices -7/23
Application 1: Givens rotation Some remarks ▸ When a Givens rotation is real, then both diagonal elements are the same. ▸ When a Givens rotation is complex, then the diagonal elements are complex conjugates of each other. ▸ A unitary matrix of the form ( −c s s c ) where the real parts of the diagonal elements have different signs, is a reflection; it is not a Givens rotation. In numerical linear algebra, a Givens rotation is a rotation in the plane spanned by two coordinates axes. ––Givens rotations are named after Wallace Givens, who introduced them to numerical analysts in the 1950s while he was working at Argonne National Laboratory. Matrix Theory Special Matrices - 7/23
Application 1:Givens rotation Some remarks When a Givens rotation is real,then both diagonal elements are the same. When a Givens rotation is complex,then the diagonal elements are complex conjugates of each other. A unitary matrix of the form where the real parts of the diagonal elements have different signs,is a reflection;it is not a Givens rotation. 奇电有这头 Matrix Theory Special Matrices -7/23
Application 1: Givens rotation Some remarks ▸ When a Givens rotation is real, then both diagonal elements are the same. ▸ When a Givens rotation is complex, then the diagonal elements are complex conjugates of each other. ▸ A unitary matrix of the form ( −c s s c ) where the real parts of the diagonal elements have different signs, is a reflection; it is not a Givens rotation. In numerical linear algebra, a Givens rotation is a rotation in the plane spanned by two coordinates axes. ––Givens rotations are named after Wallace Givens, who introduced them to numerical analysts in the 1950s while he was working at Argonne National Laboratory. Matrix Theory Special Matrices - 7/23