Peskin & Schroeder about spontaneous symmetry breaking

I am confused about how Peskin & Schroeder derive the matrix (21.39):
begin{equation}
gF^a_{ i}=frac{v}{2} left(begin{array}{ccc}
g & 0 & 0
0 & g & 0
0 & 0 & g
0 & 0 & -g’
end{array}right),
end{equation}
where $F^a_{ i} equiv T^a_{ij}phi_{0j}$ ($T^a_{ij}$ are the real anti-symmetric generators of the group $SU(2) times U(1)$, and $phi_{0j}$ is the $j$-th vacuum expectation value). Just above for an example, they say that "$T^1 phi_0$ equals $v/2$ times a unit vector in the $phi_1$ direction", but according to their definition of $T^a$, one has $T^1=-ifrac{sigma^1}{2}$ (where $sigma^1$ is the first Pauli matrix), and so
begin{equation}
T^1 phi_0 = frac{1}{sqrt{2}}
left(begin{array}{cc}
0 & -i/2
-i/2 & 0
end{array}right)
left(begin{array}{c}
0
v
end{array}right)
=
-frac{1}{sqrt{2}}left(begin{array}{c}
-iv/2
0
end{array}right),
end{equation}
which is not normalized to $1$. Furthermore, this matrix is a column of two lines, and I don’t understand how to recover their matrix (21.39) from two lines-vectors.