Is Rodrik a knight?

[Ser Morbid]

What's "the North"?

"What is love ? Bobby don't hurt me, no more"

[Abdallah]

Ser Rodrick is a Knight. The Northern Cavalry is just as good as Southern Cavalry. Chances are the idea of knighthood will continue to increase in popularity and the number of knighthoods will increase. 

[Rhaenys_Targaryen]

I'm having a debate with my friend.  According to AWOAIF there aren't really any knights in the North, but I think Rodrik was an exception, people only call him "Ser" because he's a castellan, and there are no other examples of knights in the North he can think of.  He says there is no evidence to suggest that he is.  Thoughts? 

Not only is he called "Ser" time and time again (which, btw, is not a title for a castallan, but a title for a knight), he's also described using the word "knight" on multiple occasions. Two examples below.

 

"My lady," Ser Rodrik said, "I have thought on how best to proceed while I lay abed. You must not enter the castle. I will go in your stead and bring Ser Aron to you in some safe place."

She studied the old knight as the galley drew near to a pier. Moreo was shouting in the vulgar Valyrian of the Free Cities. "You would be as much at risk as I would."

 

"Ser Rodrik Cassel is master-at-arms at Winterfell," Varys informed him. "I assure you, Lady Stark, nothing at all has been done to the good knight. He did call here early this afternoon. He visited with Ser Aron Santagar in the armory, and they talked of a certain dagger. About sunset, they left the castle together and walked to that dreadful hovel where you were staying. They are still there, drinking in the common room, waiting for your return. Ser Rodrik was very distressed to find you gone."

 

[King of the Narrow Sea]

"Are you training women here?" the burned man wanted to know. He was muscled like a bull.

"I am training knights," Ser Rodrik said pointedly. "They will have steel when they are ready. When they are of an age."