The 40 principles of invention are a suite of ideas that purport to aid in solving hard technical problems.
The principles are based on TRIZ, a theory about problem solving.
A contradiction matrix is a structured and systematic representation of basic engineering parameters of objects, or systems, such as mass, length and manufacturing tolerances.
TRIZ claims that by studying an individual parameter that is causing a problem (e.g., the mass of an object needs to be reduced), and the other parameters with which it conflicts (e.g., the lower mass would require thinner material, which is more likely to undergo catastrophic failure), solutions can be created.
Namely, the structured contents of each of the cells within the contradiction matrix, (i.e. cells fulfilled with ordered principles and identified by their order numbers) - the principles of inventions have been chosen, due to realized necessary statistical extensive studies.