from mathutils import *
vec = Vector((1.0, 2.0, 3.0, 4.0))
mat = Matrix((0.952096, -0.291454, 0.092565, 0.000000), (0.291473, 0.956482, 0.013619, 0.000000), (-0.092506, 0.014013, 0.995614, 0.000000), (0.000000, 0.000000, 0.000000, 1.000000))
a = vec * mat
b = mat * vec

>>> a
Vector((0.6468830108642578, 2.2452940940856934, 2.9223618507385254, 4.0))

>>> b
Vector((1.257524013519287, 1.6635489463806152, 3.106644868850708, 4.0))

# --------

from mathutils import *
vec = Vector((1.0, 2.0, 3.0, 4.0))
mat = Matrix((0.952096, -0.291454, 0.092565, 0.000000), (0.291473, 0.956482, 0.013619, 0.000000), (-0.092506, 0.014013, 0.995614, 0.000000), (0.000000, 0.000000, 0.000000, 1.000000))
a = vec * mat.copy().transpose()
b = vec * mat

>>> a
Vector((0.6468830108642578, 2.2452940940856934, 2.9223618507385254, 4.0))

>>> b
Vector((1.257524013519287, 1.6635489463806152, 3.106644868850708, 4.0))