using LinearAlgebra
A=2*rand(5,5).-1
R=copy(A)

# first column
v=R[:,1]
c=norm(v)
if v[1]>0
    v[1]+=c
else
    v[1]-=c
end
v/=norm(v)
R-=2*v*(v'*R)

# next column
v=R[:,2]
v[1]=0
c=norm(v)
if v[2]>0
    v[2]+=c
else
    v[2]-=c
end
v/=norm(v)
R-=2*v*(v'*R)

# third column
v=R[:,3]
v[1:2].=0
c=norm(v)
if v[3]>0
    v[3]+=c
else
    v[3]-=c
end
v/=norm(v)
R-=2*v*(v'*R)