TRIZ is a way of breaking down an engineering design problem into the thing you want to change, and the thing you can't change (a "contradiction"), then resolving it. A "TRIZ Matrix" is a reference tool that suggests ways of resolving conflicts between common design parameters (strength, weight, durability, manufacturing tolerance, etc.) based on a number of principles that have been validated over the years, like "nesting" or "prior action". Over the years, 40 standard principles (and 39 parameters) have emerged. They all have somewhat cryptic, consultant-handbooky names but make sense when you see some examples[1].

E.g., you have a beam and you want to make it stronger, but can't make it any thicker. You consult your matrix for "strength" vs "area" and get some suggestions such as "use composite materials". Or, applying the principle more generally, you try to extract techniques from the patent library or publications that resolve the problem.

[1]: https://www.triz.co.uk/files/triz_40_inventive_principles_wi...