Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It is fundamentally about solving systems of linear equations. Key Characteristics / Core Concepts Vectors: Directed line segments with magnitude and direction. Matrices: Rectangular arrays of numbers used to represent linear transformations. Linear Transformations: Functions that map vectors to … Read more
Functional analysis is a branch of mathematical analysis that studies vector spaces endowed with some kind of limit-related structure (e.g., inner product, norm, topology), along with linear functions defined on these spaces. It’s a powerful tool that connects abstract algebra, topology, and analysis, with applications throughout mathematics, engineering, and computer science. Key Characteristics / Core … Read more
Abstract algebra is the study of algebraic structures, which are sets equipped with operations that satisfy certain axioms. It moves beyond the concrete numbers and variables of elementary algebra to explore more general concepts and relationships. Key Characteristics / Core Concepts Groups: Sets with a single binary operation satisfying closure, associativity, identity, and inverse properties. … Read more