  Majorana Representation (MR) of symmetric $ N $-qubit pure states has been
used successfully in entanglement classification. Generalization of this has
been a long standing open problem due to the difficulties faced in the
construction of a Majorana like geometric representation for symmetric mixed
state. We have overcome this problem by developing a method of classifying
local unitary (LU) equivalent classes of symmetric $N$-qubit mixed states based
on the geometrical Multiaxial Representation (MAR) of the density matrix. In
addition to the two parameters defined for the entanglement classification of
the symmetric pure states based on MR, namely, diversity degree and degeneracy
configuration, we show that another parameter called rank needs to be
introduced for symmetric mixed state classification. Our scheme of
classification is more general as it can be applied to both pure and mixed
states. To bring out the similarities/ differences between the MR and MAR, $ N
$-qubit GHZ state is taken up for a detailed study. We conclude that pure state
classification based on MR is not a special case of our classification scheme
based on MAR. We also give a recipe to identify the most general symmetric
$N$-qubit pure separable states. The power of our method is demonstrated using
several well known examples of symmetric two qubit pure and mixed states as
well as three qubit pure states. Classification of uniaxial, Biaxial and
triaxial symmetric two qubit mixed states which can be produced in the
laboratory is studied in detail.
