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givens

Givens transformation

Syntax

U=givens(xy)
U=givens(x,y)
[U,c]=givens(xy)
[U,c]=givens(x,y)

Arguments

x,y

two real or complex numbers

xy

real or complex size 2 column vector

U

2x2 unitary matrix

c

real or complex size 2 column vector

Description

U= givens(x, y) or U = givens(xy) with xy = [x;y] returns a 2x2 unitary matrix U such that:

U*xy=[r;0]=c.

Note that givens(x,y) and givens([x;y]) are equivalent.

Examples

A=[3,4;5,6];
U=givens(A(:,1));
U*A

See also


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