Subspace

A subspace is a specific type of subset within a vector space that retains the fundamental properties of the original space. This means it is closed under addition and scalar multiplication—if you add any two vectors in the subspace or multiply a vector by a number, the result stays within the subspace. Examples include lines or planes within higher-dimensional spaces. Subspaces are important because they help break down complex spaces into manageable parts, enabling easier analysis and understanding of their structure, such as in solving systems of equations or studying geometric and algebraic properties.