Lady Ice-Heart

From what I understand in regards to the title of Master-at-Arms, their duties are to take charge of training and drills of recruits as well as maintaining their respective armories (as well as being heavy cavalry when push comes to shove). It's honestly huge that we have a Companion with an official duty and title and it speaks worlds to Vilkas as a character when that was specifically assigned to him (especially with older, more experienced Circle members around!)

Some small things I like to think about in regards to his role:

Skjor was the former Master-at-Arms who passed his role along to Vilkas, who was widely regarded as his recruit in earlier times (especially as Kodlak assumed the role of Harbinger, and likely did not engage with the training as much as the Circle did). Vilkas was already the oldest and most accomplished "whelp" of his time, and his dedication and ambition would not go unnoticed – especially when he began as the smallest and weakest in comparison to those around him (I like to think he is a short king for a Nord). He was rewarded this status after an honorable multi-round duel with different weapons to truly show his mastery over the articles of the Jorrvaskr armory, in which he came out the other side victorious. It was one of the few times Skjor ever expressed how proud he was to the young man despite his loss.

Vilkas really is a harsh mentor. He expects all those he trains to have the same level of discipline that he does. He rouses the whelps in the early hours of the morning and drills them on maintaining their own weapons and armor, before and after their rounds in the yard. He does not suffer foolishness or laziness – slack off, and you'll have thrice the work tossed on you. He keeps a tight schedule for the days, the hours, and what types of training he'll be putting people through in all that time.

Vilkas learned much of his teaching ways from Skjor, who most certainly viewed himself as the hammer that shaped the weapons his whelps aspired to be. And a hammer has to be harsh. Kodlak's influence shows in the way Vilkas speaks: he's well-read and well-spoken, and readily takes time to spread wisdom orally. He strikes a good balance between Skjor's abrasiveness and brutal realism and Kodlak's more philosophical and gregarious personality, interested in raising up not just warriors but true Companions, who value honor, culture, and tradition.

Most recruits, of course, really don't like him. For better or worse his attitude can scare many young recruits off, but in his mind, it's about culling the milkdrinkers and snowberries while they can still get out alive. As even Farkas says, "this can be a rough life" — and when the brothers started out as young as they did in Jorrvaskr, I can only imagine how many people they've seen die, the ways they've seen people die. People they knew. People they possibly even cared for. (Jergen, of course, is a given in this regard).

Lots of yap… now, for as the public would view this man versus how he views himself…

Companions of Jorrvaskr are widely respected in all of Skyrim, and by lore, they seem to have been intended not only as a standing source of aid for the citizenship, and pride for the Nord people's martial prowess, but even a cultural/historical pylon. I think Vilkas embodies all spheres of what makes the Companions so special, and maybe the one thing holding him back from the arms of public adoration is how unpleasant his upfront personality is. In Whiterun, he's definitely not known for his brilliant personality (honestly? he might be known as the Asshole Companion) but he's known to be a man of honor all the same, and is the guy who will get the job done and done right (and yes, even a highly desired bachelor - how can anyone resist a dark-haired, mysterious warrior with all the sadness of the world in his eyes?).

As for himself… well… I see a man who is horribly insecure in Vilkas.

When you meet him, he presents himself as aloof and as a simple mercenary in it for only the Holy Septim. He says he thinks the war ravaging his homeland is pretty much pointless, not presenting him a good enough reason to fight. The gods might as well be dead to him. The man who rescued him and his brother decided to wander off and die somewhere instead of stay home with his two adopted kids - why should Vilkas care about him? Jergen clearly didn't care enough to stay, so he's not his problem anymore. He'll boast on occasion about having hunted one of every living thing in Skyrim and sends his lessers on errands, even asks you to show respect once asked about his past. You get the most honest presentation of him by asking him about his thoughts on the Companions and his personal history: he holds great respect for Ysgramor as their founder, and he loves his brother (as well as that note of resentment about Jergen).