Start on the right side of North Arete. After the approach up the narrow snow gully (just left of West Couloir) climb in a big left-facing dihedral (that is likely to have some snow or ice in it). Climb up the dihedral. Than traverse left to a ledge, and up to the second dihedral with a wide crack. This 2nd dihedral could be reached from the left side of the North Arete as well. Climb up this dihedral (crux) to a head-wall. There is a block to sling right under the headwall. Sling this block and climb up the headwall directly taking the line of your desire. I took the line right over the block we used for anchor. Had to climb a ways up before getting in first useful protection, but climbing wasn't too bad. Maybe 5.6-7. After that simul climb or solo the 3-4th class ridge to the summit of Matterhorn. Descent East Couloir.
Cams: 1-2 set of cams up to #2. #4-6 (to protect the second dihedral)optional, if you want to feel safe. We did not have any pieces bigger than # 2 and climbing in the dihedral was PG13. Two chock stones could be slung with a double length runner.
A set of nuts
Desire for a cool adventure