ARIZ (Algorithm for Inventive Problem Solving) - is a systematic procedure for identifying solutions without apparent contradictions.
(Dr.Prakash R.Apte. Introduction to TRIZ.Innovative Problem Solving)

Contradiction appears in the process, where one desirable property of the technology or technical system (A) is improved and another desirable property (B) is worsen. (Semyon D. Savransky (2000). ENGINEERING OF CREATIVITY: Introduction to TRIZ Methodology of Inventive Problem Solving)

Contradiction Matrix - a 39 x 39 Matrix defined by the 39 Engineering Parameters which shows which of the 40 Inventive Principles other engineers have previously successfully used to solve contradictions similar to the ones being analysed.

Inventive Principles - the 40 solutions to any contradiction - all the ways Altshuller discovered to eliminate technical contradictions.  (http://baetriz.co.uk/glossary.htm)

TRIZ - methodology, tool set, knowledge base, and model-based technology for generating innovative ideas and solutions for problem solving. TRIZ provides tools and methods for use in problem formulation, system analysis, failure analysis, and patterns of system evolution. (http://en.wikipedia.org/wiki/TRIZ)

39 Engineering Parameters -  the fundamental descriptors used to define any engineering contradiction, such as STRENGTH and WEIGHT.