Mathews' men held on for a draw in the series-opener at Lord's, with last man Nuwan Pradeep surviving five balls in the final over to ensure Sri Lanka were not bowled out in their second innings.
The tourists now hope to build on their first-Test performance by securing victory in Yorkshire.
All-rounder Mathews told a press conference on Thursday: "We've been taking a lot of positives from that game, the way we fought, the way the boys showed their character was good."
"It's going to be our last game here in England for this summer and we look forward to giving them a good fight and hopefully winning it, and ending on a good note."
The Headingley wicket is expected to provide greater assistance to the bowlers, after both sides were faced with a flat pitch at Lord's.
However, Mathews does not feel Sri Lanka will be required to adopt a change in approach when England are batting.
"I don't think there will be a departure from bowling line and length. We'll try and stick to our basics," he said.
"If needed, we'll try to change our plans and tactics a little bit, but all in all our strength is to keep it line and length and bowl in those good areas.
"But Test cricket is all about challenging the opposition. It's about thinking a step further than the batsman. If you have to make those tactical changes we will.
"I think the pitch gives us a chance as well. We've got some good seamers.
"Rather than make it a flat wicket, it's always good to have a sporting wicket where both teams have their chances."