import bpy
from mathutils import Vector

cam = bpy.data.objects['Camera']
up = cam.matrix_world.to_quaternion() * Vector((0.0, 1.0, 0.0))
cam_direction = cam.matrix_world.to_quaternion() * Vector((0.0, 0.0, -1.0))

2.8x

import bpy
from mathutils import Vector

cam = bpy.data.objects['Camera']
up = cam.matrix_world.to_quaternion() @ Vector((0.0, 1.0, 0.0))
cam_direction = cam.matrix_world.to_quaternion() @ Vector((0.0, 0.0, -1.0))

2.7x

import bpy
from mathutils import Vector

cam = bpy.data.objects['Camera']
up = cam.matrix_world.to_quaternion() * Vector((0.0, 1.0, 0.0))
cam_direction = cam.matrix_world.to_quaternion() * Vector((0.0, 0.0, -1.0))

import bpy
from mathutils import Vector

cam = bpy.data.objects['Camera']
up = cam.matrix_world * Vector((0.0, 1.0, 0.0))
cam_direction = cam.matrix_world * Vector((0.0, 0.0, -1.0))

import bpy
from mathutils import Vector

cam = bpy.data.objects['Camera']
up = cam.matrix_world.to_quaternion() * Vector((0.0, 1.0, 0.0))
cam_direction = cam.matrix_world.to_quaternion() * Vector((0.0, 0.0, -1.0))