Fundamentals of the New Neutrosophic Matrices

The New Neutrosophic Matrices provides a mathematical extension of classical and fuzzy matrix theory that incorporates the element of indeterminacy alongside truth and falsity. Neutrosophic logic, pioneered by FlorentinSmarandache, provides a richer framework for dealing with uncertainty and vagueness in real-world data. This study explores the definitions, classifications, and algebraic operations onneutrosophic matrices, including addition, multiplication, scalar operations, and the formation of identities.A comparative analysis is presented to highlight the distinctions between classical, fuzzy, and neutrosophic matrices. From the concepts, potential applications could be proposed most especially, for more problem solving as well as for future exploration.Findingsaffirmthat neutrosophic matrices offer aversatile and robust mathematical tool for modeling uncertainty in various fields such as scientific, engineering technology and other life endeavors involving decision-making and problem solving.