  We observe the anisotropy of the power spectral tensor of magnetic field
fluctuations in the fast solar wind for the first time. In heliocentric RTN
coordinates the power in each element of the tensor has a unique dependence on
the angle between the magnetic field and velocity of the solar wind (\theta)
and the angle of the vector in the plane perpendicular to the velocity (\phi).
We derive the geometrical effect of the high speed flow of the solar wind past
the spacecraft on the power spectrum in the frame of the plasma P(k) to arrive
at the observed power spectrum P(f,\theta,\phi) based on a scalar field
description of turbulence theory. This allows us to predict the variation in
the \phi direction and compare it to the data. We then transform the
observations from RTN coordinates to magnetic-field-aligned coordinates. The
observed reduced power spectral tensor matches the theoretical predictions we
derive in both RTN and field-aligned coordinates which means that the local
magnetic field we calculate with wavelet envelope functions is an accurate
representation of the physical axis of symmetry for the turbulence and implies
that on average the turbulence is axi-symmetric. We also show that we can
separate the dominant toroidal component of the turbulence from the smaller but
significant poloidal component and that these have different power anisotropy.
We also conclude that the magnetic helicity is anisotropic and mostly
two-dimensional, arising from wavevectors largely confined to the plane
perpendicular to B.
