Both endured difficulties in 2014 and are committed to bouncing back.
Peterson made the Pro Bowl as a cornerback for the third consecutive time, but last season was below his standards. He gave up eight touchdowns and especially struggled in the first month.
Mathieu had difficulty returning from a severe knee injury suffered in December of 2013.
"I cannot wait until the season starts to put all this criticism (to rest): 'He's lost a step,' or 'Can Tyrann stay healthy?'" Peterson said. "There's a lot of things that we cannot wait to get on the field to show the world."
Part of Peterson's problem was physical. He gained weight and felt sluggish. Early in the season, doctors diagnosed him with type 1 diabetes, he said.
The diabetes is under control and Peterson said he's lost "a lot" of weight from this time last season. He wouldn't say how much. He's listed at 219 pounds, the same as last year, but appears to be closer to 200.
"I was just a step behind in making those plays and that was due to my weight," he said. "That was due to my sluggish movement and all that. Now that's under control and behind me."
--It turns out his left knee wasn't the only thing quarterback Carson Palmer was rehabbing this offseason. He also worked hard to strengthen his right shoulder, which was injured in the first game of 2014.
Palmer worked with Phoenix physical therapist Brett Fischer, who consults with the Cardinals and works with athletes in other sports, including baseball.
Even though his shoulder didn't require surgery, Palmer underwent a post-surgery protocol on the shoulder. The difference in arm strength has been noticeable early in camp.
"I feel my arm has gotten stronger, just from all the workouts I've been doing," Palmer said. "It feels as strong as it's ever been, maybe stronger."
Palmer has been very sharp so far in camp and appears unconcerned about his health.
"He's a lot of fun to watch right now," head coach Bruce Arians said.
--The Cardinals believe this is their most talented team in years, but they do have weaknesses. Tight end remains a concern. Jermaine Gresham was signed last week but is recovering from back surgery in March.
Troy Niklas, a second-round pick a year ago, didn't practice early in camp due to a hamstring injury suffered the week before camp.
"I was doing a lot of running and probably should have rested my legs a little more," said Niklas, a second-round pick last year. "I'm still new at the NFL and still learning how to become a professional athlete. Sometimes you push yourself too hard when you're training."
Both passed physicals Monday and were cleared to practice, but will be brought along slowly.
The starter now is Darren Fells, who might have been the regular starter anyway. He started the final four games of 2014 and played well. A former college basketball player, Fells has proven to be a solid blocker as well as a dependable receiver.