A={{1,1,1,1,1,1,1},{0.5,0.33333333333333331,0.25,0.20000000000000001,0.16666666666666666,0.14285714285714285,0.125},{0.33333333333333331,0.25,0.20000000000000001,0.16666666666666666,0.14285714285714285,0.125,0.1111111111111111},{0.25,0.20000000000000001,0.16666666666666666,0.14285714285714285,0.125,0.1111111111111111,0.10000000000000001},{0.20000000000000001,0.16666666666666666,0.14285714285714285,0.125,0.1111111111111111,0.10000000000000001,0.090909090909090912}};
A//MatrixForm

H[u_]:=IdentityMatrix[Length[u]]-2/u.u KroneckerProduct[u,u]

v0={1,-0.60762521851076512,-0.60762521851076512,-0.60762521851076512,-0.60762521851076512,-0.60762521851076512,-0.60762521851076512};
Chop[A.H[v0]]//MatrixForm

u0={0,1,-1.4952198070674976,-1.2326968908072145,-1.0537039933570211};
Chop[H[u0].A.H[v0]]//MatrixForm

v1={0,1,-2.0400400885411587,-1.3645737495441417,-0.8902838360795744,-0.53788988669098869,-0.26527977681757903};
Chop[H[u0].A.H[v0].H[v1]]//MatrixForm

u1={0,0,1,-4.0264831822186054,-1.5562706147408738};
Chop[H[u1].H[u0].A.H[v0].H[v1]]//MatrixForm

v2={0,0,1,0.11256490602694814,-0.10599453274564564,-0.30804716604731053,-0.48807119906754026};
Chop[H[u1].H[u0].A.H[v0].H[v1].H[v2]]//MatrixForm

u2={0,0,0,1,-0.25238223936608356};
Chop[H[u2].H[u1].H[u0].A.H[v0].H[v1].H[v2]]//MatrixForm

v3={0,0,0,1,0.089296782824959925,0.39421403276529532,0.84205368670737646};
Chop[H[u2].H[u1].H[u0].A.H[v0].H[v1].H[v2].H[v3]]//MatrixForm

v4={0,0,0,0,1,-1.0736125613887906,2.0321085005643256};
Chop[H[u2].H[u1].H[u0].A.H[v0].H[v1].H[v2].H[v3].H[v4]]//MatrixForm

B={{2.6457513110645907,0,0,0,0,0,0},{0.98522806266180785,0.40168002820413445,0,0,0,0,0},{0,0.08752539295361457,0.023923558389346716,0,0,0,0},{0,0,0.0035527353431211248,0.0008042672826898623,0,0,0},{0,0,0,-7.555997080246309*^-05,1.3631442076118568*^-05,0,0}};
B//MatrixForm

A={{1,1,1},{0.5,0.33333333333333331,0.25}};
A//MatrixForm

v0={1,-1.3660254037844386,-1.3660254037844386}
Chop[A.H[v0]]//MatrixForm

v1={0,1,-4.3499346972838113}
Chop[A.H[v0].H[v1]]//MatrixForm

Q=H[v1].H[v0];
Q//MatrixForm

L={{1.7320508075688772,0,0},{0.6254627916220945,0.18002057495577398,0}};
L//MatrixForm

Chop[A-L.Q\[Transpose]]//MatrixForm

H[v1]//MatrixForm